Math / Geometry

QuestionFind the value of $x$ .

Studdy Solution

STEP 1

What is this asking? We need to find the missing angle inside the triangle, labeled $x$ . Watch out! Don't get tricked by the angle outside the triangle!
Remember the relationship between exterior and interior angles.

STEP 2

1. Exterior Angle Theorem
2. Solve for x

STEP 3

The Exterior Angle Theorem says that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Basically, the outside angle is the sum of the two inside angles farthest from it.

STEP 4

In our triangle, the exterior angle is $125^\circ$ .
The two nonadjacent interior angles are $36^\circ$ and $x^\circ$ .
So, we can write the equation: $125^\circ = 36^\circ + x^\circ$ .

STEP 5

To get $x$ by itself, we need to subtract $36^\circ$ from both sides of the equation.
This keeps everything balanced!

STEP 6

$125^\circ - 36^\circ = x^\circ$ $89^\circ = x^\circ$ So, $x = \mathbf{89^\circ}$ !

STEP 7

The value of $x$ is $\mathbf{89^\circ}$ .

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QuestionFind the value of $x$ .

Studdy Solution

STEP 1

What is this asking? We need to find the missing angle inside the triangle, labeled $x$ . Watch out! Don't get tricked by the angle outside the triangle!
Remember the relationship between exterior and interior angles.

STEP 2

1. Exterior Angle Theorem
2. Solve for x

STEP 3

The Exterior Angle Theorem says that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Basically, the outside angle is the sum of the two inside angles farthest from it.

STEP 4

In our triangle, the exterior angle is $125^\circ$ .
The two nonadjacent interior angles are $36^\circ$ and $x^\circ$ .
So, we can write the equation: $125^\circ = 36^\circ + x^\circ$ .

STEP 5

To get $x$ by itself, we need to subtract $36^\circ$ from both sides of the equation.
This keeps everything balanced!

STEP 6

$125^\circ - 36^\circ = x^\circ$ $89^\circ = x^\circ$ So, $x = \mathbf{89^\circ}$ !

STEP 7

The value of $x$ is $\mathbf{89^\circ}$ .

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QuestionFind the value of xxx.

Studdy Solution

STEP 1

What is this asking? We need to find the missing angle inside the triangle, labeled xxx. Watch out! Don't get tricked by the angle *outside* the triangle!Remember the relationship between exterior and interior angles.

STEP 2

1. Exterior Angle Theorem2. Solve for *x*

STEP 3

The **Exterior Angle Theorem** says that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.Basically, the outside angle is the sum of the two inside angles *farthest* from it.

STEP 4

In our triangle, the exterior angle is 125∘125^\circ125∘.The two nonadjacent interior angles are 36∘36^\circ36∘ and x∘x^\circx∘.So, we can write the equation: 125∘=36∘+x∘125^\circ = 36^\circ + x^\circ125∘=36∘+x∘.

STEP 5

To get xxx by itself, we need to subtract 36∘36^\circ36∘ from *both* sides of the equation.This keeps everything balanced!

STEP 6

125∘−36∘=x∘125^\circ - 36^\circ = x^\circ125∘−36∘=x∘ 89∘=x∘89^\circ = x^\circ89∘=x∘ So, x=89∘x = \mathbf{89^\circ}x=89∘!

STEP 7

The value of xxx is 89∘\mathbf{89^\circ}89∘.

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QuestionFind the value of $x$ .

What is this asking? We need to find the missing angle inside the triangle, labeled $x$ . Watch out! Don't get tricked by the angle outside the triangle!
Remember the relationship between exterior and interior angles.

1. Exterior Angle Theorem
2. Solve for x

The Exterior Angle Theorem says that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Basically, the outside angle is the sum of the two inside angles farthest from it.

In our triangle, the exterior angle is $125^\circ$ .
The two nonadjacent interior angles are $36^\circ$ and $x^\circ$ .
So, we can write the equation: $125^\circ = 36^\circ + x^\circ$ .

To get $x$ by itself, we need to subtract $36^\circ$ from both sides of the equation.
This keeps everything balanced!

$125^\circ - 36^\circ = x^\circ$ $89^\circ = x^\circ$ So, $x = \mathbf{89^\circ}$ !

The value of $x$ is $\mathbf{89^\circ}$ .