Math / Geometry

Question5. In parallelogram HIJK, the measure of angle H is 45 . a. Find the measure of angle $J$ . Explain or show how you know. A diagram may be helpful. b. Find the measure of angle $K$ . Explain or show how you know.
6. The $m \angle Q=70^{\circ}$ . Find the $m \angle P$ . You must explain or show how you arrived at your answer.

Studdy Solution

STEP 1

What is this asking? We need to find the angles in a parallelogram and another seemingly unrelated angle $\angle P$ , given some other angles. Watch out! Don't forget the relationships between angles in a parallelogram!
Also, make sure your explanations are crystal clear.

STEP 2

1. Parallelogram Angles
2. Mystery Angle

STEP 3

Alright, let's tackle this parallelogram problem!
We're given parallelogram HIJK and told that the measure of $\angle H$ is $\angle H = 45^\circ$ .
We need to find the measures of $\angle J$ and $\angle K$ .

STEP 4

Remember, in a parallelogram, adjacent angles are supplementary, meaning they add up to $180^\circ$ .
Also, opposite angles are congruent, meaning they have the same measure.

STEP 5

Since $\angle H$ and $\angle J$ are opposite angles, they have the same measure.
So, $\angle J = \angle H = 45^\circ$ .
Boom!

STEP 6

Now, let's find $\angle K$ .
Since $\angle H$ and $\angle K$ are adjacent angles, they are supplementary.
This means $\angle H + \angle K = 180^\circ$ .
We know $\angle H = 45^\circ$ , so $45^\circ + \angle K = 180^\circ$ .

STEP 7

To find $\angle K$ , we subtract $45^\circ$ from both sides of the equation: $\angle K = 180^\circ - 45^\circ = 135^\circ$ .
Awesome!

STEP 8

Now, for the mystery angle!
We're given that $m\angle Q = 70^\circ$ and we need to find $m\angle P$ .
Hmm, this seems disconnected from the parallelogram, but let's assume they're related somehow.
Maybe they're vertical angles?

STEP 9

If $\angle P$ and $\angle Q$ are vertical angles, then they are congruent, meaning they have the same measure.
So, if $m\angle Q = 70^\circ$ , then $m\angle P = 70^\circ$ as well!

STEP 10

For parallelogram HIJK, $\angle J = 45^\circ$ and $\angle K = 135^\circ$ .
For the mystery angles, assuming they're vertical angles, $m\angle P = 70^\circ$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the angles in a parallelogram and another seemingly unrelated angle $\angle P$ , given some other angles. Watch out! Don't forget the relationships between angles in a parallelogram!
Also, make sure your explanations are crystal clear.

STEP 2

1. Parallelogram Angles
2. Mystery Angle

STEP 3

Alright, let's tackle this parallelogram problem!
We're given parallelogram HIJK and told that the measure of $\angle H$ is $\angle H = 45^\circ$ .
We need to find the measures of $\angle J$ and $\angle K$ .

STEP 4

Remember, in a parallelogram, adjacent angles are supplementary, meaning they add up to $180^\circ$ .
Also, opposite angles are congruent, meaning they have the same measure.

STEP 5

Since $\angle H$ and $\angle J$ are opposite angles, they have the same measure.
So, $\angle J = \angle H = 45^\circ$ .
Boom!

STEP 6

Now, let's find $\angle K$ .
Since $\angle H$ and $\angle K$ are adjacent angles, they are supplementary.
This means $\angle H + \angle K = 180^\circ$ .
We know $\angle H = 45^\circ$ , so $45^\circ + \angle K = 180^\circ$ .

STEP 7

To find $\angle K$ , we subtract $45^\circ$ from both sides of the equation: $\angle K = 180^\circ - 45^\circ = 135^\circ$ .
Awesome!

STEP 8

Now, for the mystery angle!
We're given that $m\angle Q = 70^\circ$ and we need to find $m\angle P$ .
Hmm, this seems disconnected from the parallelogram, but let's assume they're related somehow.
Maybe they're vertical angles?

STEP 9

If $\angle P$ and $\angle Q$ are vertical angles, then they are congruent, meaning they have the same measure.
So, if $m\angle Q = 70^\circ$ , then $m\angle P = 70^\circ$ as well!

STEP 10

For parallelogram HIJK, $\angle J = 45^\circ$ and $\angle K = 135^\circ$ .
For the mystery angles, assuming they're vertical angles, $m\angle P = 70^\circ$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the angles in a parallelogram and another seemingly unrelated angle ∠P\angle P∠P, given some other angles. Watch out! Don't forget the relationships between angles in a parallelogram!Also, make sure your explanations are crystal clear.

STEP 2

1. Parallelogram Angles2. Mystery Angle

STEP 3

Alright, let's tackle this parallelogram problem!We're given parallelogram *HIJK* and told that the measure of ∠H\angle H∠H is ∠H=45∘\angle H = 45^\circ∠H=45∘.We need to find the measures of ∠J\angle J∠J and ∠K\angle K∠K.

STEP 4

Remember, in a parallelogram, **adjacent angles** are *supplementary*, meaning they add up to 180∘180^\circ180∘.Also, **opposite angles** are *congruent*, meaning they have the same measure.

STEP 5

Since ∠H\angle H∠H and ∠J\angle J∠J are opposite angles, they have the same measure.So, ∠J=∠H=45∘\angle J = \angle H = 45^\circ∠J=∠H=45∘.Boom!

STEP 6

STEP 7

To find ∠K\angle K∠K, we subtract 45∘45^\circ45∘ from both sides of the equation: ∠K=180∘−45∘=135∘\angle K = 180^\circ - 45^\circ = 135^\circ∠K=180∘−45∘=135∘.Awesome!

STEP 8

Now, for the mystery angle!We're given that m∠Q=70∘m\angle Q = 70^\circm∠Q=70∘ and we need to find m∠Pm\angle Pm∠P.Hmm, this seems disconnected from the parallelogram, but let's assume they're related somehow.Maybe they're vertical angles?

STEP 9

If ∠P\angle P∠P and ∠Q\angle Q∠Q are vertical angles, then they are congruent, meaning they have the same measure.So, if m∠Q=70∘m\angle Q = 70^\circm∠Q=70∘, then m∠P=70∘m\angle P = 70^\circm∠P=70∘ as well!

STEP 10

For parallelogram *HIJK*, ∠J=45∘\angle J = 45^\circ∠J=45∘ and ∠K=135∘\angle K = 135^\circ∠K=135∘.For the mystery angles, assuming they're vertical angles, m∠P=70∘m\angle P = 70^\circm∠P=70∘.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the angles in a parallelogram and another seemingly unrelated angle $\angle P$ , given some other angles. Watch out! Don't forget the relationships between angles in a parallelogram!
Also, make sure your explanations are crystal clear.

1. Parallelogram Angles
2. Mystery Angle

Alright, let's tackle this parallelogram problem!
We're given parallelogram HIJK and told that the measure of $\angle H$ is $\angle H = 45^\circ$ .
We need to find the measures of $\angle J$ and $\angle K$ .

Remember, in a parallelogram, adjacent angles are supplementary, meaning they add up to $180^\circ$ .
Also, opposite angles are congruent, meaning they have the same measure.

Since $\angle H$ and $\angle J$ are opposite angles, they have the same measure.
So, $\angle J = \angle H = 45^\circ$ .
Boom!

To find $\angle K$ , we subtract $45^\circ$ from both sides of the equation: $\angle K = 180^\circ - 45^\circ = 135^\circ$ .
Awesome!

Now, for the mystery angle!
We're given that $m\angle Q = 70^\circ$ and we need to find $m\angle P$ .
Hmm, this seems disconnected from the parallelogram, but let's assume they're related somehow.
Maybe they're vertical angles?

If $\angle P$ and $\angle Q$ are vertical angles, then they are congruent, meaning they have the same measure.
So, if $m\angle Q = 70^\circ$ , then $m\angle P = 70^\circ$ as well!

For parallelogram HIJK, $\angle J = 45^\circ$ and $\angle K = 135^\circ$ .
For the mystery angles, assuming they're vertical angles, $m\angle P = 70^\circ$ .