Math / Geometry

Question11. Using the triangle below, set up and solve an equation in order to find the value of $x$ .
12. Find the measure of the largest angle in the triangle shown.

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ using the right triangle, and then use that value to find the biggest angle in the other triangle. Watch out! Don't forget that angles in a right triangle add up to $90^\circ$ and angles in any triangle add up to $180^\circ$ !

STEP 2

1. Solve for x
2. Find the largest angle

STEP 3

Alright, so we've got this right triangle, and we know two of its angles: $(15x)^\circ$ and $(8x - 2)^\circ$ .
Since it's a right triangle, the third angle is $90^\circ$ !

STEP 4

Now, here's the magic: all the angles in a triangle always add up to $180^\circ$ .
So, let's write that down as an equation: $(15x) + (8x - 2) + 90 = 180$

STEP 5

Time to combine like terms!
We've got $15x$ and $8x$ , which add up to $23x$ .
And we've got $-2$ and $90$ , which make $88$ .
So, our equation becomes: $23x + 88 = 180$

STEP 6

To isolate our $x$ term, let's subtract $88$ from both sides of the equation: $23x + 88 - 88 = 180 - 88$ $23x = 92$

STEP 7

Almost there!
Now, we divide both sides by $23$ to find the value of $x$ : $\frac{23x}{23} = \frac{92}{23}$ $x = 4$ Woohoo! We found that $x = 4$ !

STEP 8

Okay, so we know $x = 4$ , and we need to find the largest angle in the other triangle.
Its angles are $(24x)^\circ$ , $(21x)^\circ$ , and $(15x)^\circ$ .

STEP 9

Let's substitute $x = 4$ into each angle: $24 \cdot 4 = 96$ $21 \cdot 4 = 84$ $15 \cdot 4 = 60$ So, the angles are $96^\circ$ , $84^\circ$ , and $60^\circ$ .

STEP 10

The largest angle is clearly $96^\circ$ !

STEP 11

The value of $x$ is $4$ , and the largest angle in the second triangle is $96^\circ$ .

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Question11. Using the triangle below, set up and solve an equation in order to find the value of $x$ .
12. Find the measure of the largest angle in the triangle shown.

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ using the right triangle, and then use that value to find the biggest angle in the other triangle. Watch out! Don't forget that angles in a right triangle add up to $90^\circ$ and angles in any triangle add up to $180^\circ$ !

STEP 2

1. Solve for x
2. Find the largest angle

STEP 3

Alright, so we've got this right triangle, and we know two of its angles: $(15x)^\circ$ and $(8x - 2)^\circ$ .
Since it's a right triangle, the third angle is $90^\circ$ !

STEP 4

Now, here's the magic: all the angles in a triangle always add up to $180^\circ$ .
So, let's write that down as an equation: $(15x) + (8x - 2) + 90 = 180$

STEP 5

Time to combine like terms!
We've got $15x$ and $8x$ , which add up to $23x$ .
And we've got $-2$ and $90$ , which make $88$ .
So, our equation becomes: $23x + 88 = 180$

STEP 6

To isolate our $x$ term, let's subtract $88$ from both sides of the equation: $23x + 88 - 88 = 180 - 88$ $23x = 92$

STEP 7

Almost there!
Now, we divide both sides by $23$ to find the value of $x$ : $\frac{23x}{23} = \frac{92}{23}$ $x = 4$ Woohoo! We found that $x = 4$ !

STEP 8

Okay, so we know $x = 4$ , and we need to find the largest angle in the other triangle.
Its angles are $(24x)^\circ$ , $(21x)^\circ$ , and $(15x)^\circ$ .

STEP 9

Let's substitute $x = 4$ into each angle: $24 \cdot 4 = 96$ $21 \cdot 4 = 84$ $15 \cdot 4 = 60$ So, the angles are $96^\circ$ , $84^\circ$ , and $60^\circ$ .

STEP 10

The largest angle is clearly $96^\circ$ !

STEP 11

The value of $x$ is $4$ , and the largest angle in the second triangle is $96^\circ$ .

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Question11. Using the triangle below, set up and solve an equation in order to find the value of xxx.12. Find the measure of the largest angle in the triangle shown.

Studdy Solution

STEP 1

What is this asking? We need to find the value of xxx using the right triangle, and then use that value to find the biggest angle in the other triangle. Watch out! Don't forget that angles in a right triangle add up to 90∘90^\circ90∘ and angles in *any* triangle add up to 180∘180^\circ180∘!

STEP 2

1. Solve for *x*2. Find the largest angle

STEP 3

Alright, so we've got this right triangle, and we know two of its angles: (15x)∘(15x)^\circ(15x)∘ and (8x−2)∘(8x - 2)^\circ(8x−2)∘.Since it's a right triangle, the third angle is 90∘90^\circ90∘!

STEP 4

Now, here's the magic: all the angles in a triangle *always* add up to 180∘180^\circ180∘.So, let's write that down as an equation: (15x)+(8x−2)+90=180 (15x) + (8x - 2) + 90 = 180 (15x)+(8x−2)+90=180

STEP 5

Time to **combine like terms**!We've got 15x15x15x and 8x8x8x, which add up to 23x23x23x.And we've got −2-2−2 and 909090, which make 888888.So, our equation becomes: 23x+88=180 23x + 88 = 180 23x+88=180

STEP 6

To **isolate** our xxx term, let's subtract 888888 from both sides of the equation: 23x+88−88=180−88 23x + 88 - 88 = 180 - 88 23x+88−88=180−88 23x=92 23x = 92 23x=92

STEP 7

Almost there!Now, we **divide** both sides by 232323 to find the **value of** xxx: 23x23=9223 \frac{23x}{23} = \frac{92}{23} 2323x​=2392​ x=4 x = 4 x=4Woohoo! We found that x=4x = 4x=4!

STEP 8

Okay, so we know x=4x = 4x=4, and we need to find the largest angle in the other triangle.Its angles are (24x)∘(24x)^\circ(24x)∘, (21x)∘(21x)^\circ(21x)∘, and (15x)∘(15x)^\circ(15x)∘.

STEP 9

Let's **substitute** x=4x = 4x=4 into each angle: 24⋅4=96 24 \cdot 4 = 96 24⋅4=96 21⋅4=84 21 \cdot 4 = 84 21⋅4=8415⋅4=60 15 \cdot 4 = 60 15⋅4=60So, the angles are 96∘96^\circ96∘, 84∘84^\circ84∘, and 60∘60^\circ60∘.

STEP 10

The **largest angle** is clearly 96∘96^\circ96∘!

STEP 11

The value of xxx is 444, and the largest angle in the second triangle is 96∘96^\circ96∘.

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Question11. Using the triangle below, set up and solve an equation in order to find the value of $x$ .
12. Find the measure of the largest angle in the triangle shown.

What is this asking? We need to find the value of $x$ using the right triangle, and then use that value to find the biggest angle in the other triangle. Watch out! Don't forget that angles in a right triangle add up to $90^\circ$ and angles in any triangle add up to $180^\circ$ !

1. Solve for x
2. Find the largest angle

Alright, so we've got this right triangle, and we know two of its angles: $(15x)^\circ$ and $(8x - 2)^\circ$ .
Since it's a right triangle, the third angle is $90^\circ$ !

Now, here's the magic: all the angles in a triangle always add up to $180^\circ$ .
So, let's write that down as an equation: $(15x) + (8x - 2) + 90 = 180$

Time to combine like terms!
We've got $15x$ and $8x$ , which add up to $23x$ .
And we've got $-2$ and $90$ , which make $88$ .
So, our equation becomes: $23x + 88 = 180$

To isolate our $x$ term, let's subtract $88$ from both sides of the equation: $23x + 88 - 88 = 180 - 88$ $23x = 92$

Almost there!
Now, we divide both sides by $23$ to find the value of $x$ : $\frac{23x}{23} = \frac{92}{23}$ $x = 4$ Woohoo! We found that $x = 4$ !

Okay, so we know $x = 4$ , and we need to find the largest angle in the other triangle.
Its angles are $(24x)^\circ$ , $(21x)^\circ$ , and $(15x)^\circ$ .

Let's substitute $x = 4$ into each angle: $24 \cdot 4 = 96$ $21 \cdot 4 = 84$ $15 \cdot 4 = 60$ So, the angles are $96^\circ$ , $84^\circ$ , and $60^\circ$ .

The largest angle is clearly $96^\circ$ !

The value of $x$ is $4$ , and the largest angle in the second triangle is $96^\circ$ .