HELP. I can not figure this out!

Question

Find the measure of each angle in Triangle ABC. m∠a=(48−x)°m∠b=(9x−38)°m∠c=90°

Answer 1

The very important rule that applies here is that the sum of the three angles of a triangle is 180°.

Given:

m∠a=(48−x)°

m∠b=(9x−38)°

m∠c=90° Here is one answer.

(m∠a ) + (m∠b) + (m∠c) = 180°

(m∠a ) + (m∠b) + 90° = 180°

(m∠a ) + (m∠b) = 90°

(48-x) + (9x-38) = 90°

8x + 10 = 90°

8x = 80°

x = 10°

So, m∠a=(48−x)° = 38° Second answer.

m∠b=(9x−38)° = (90 - 38)° = 52° Third answer.

Check:

Does 38° + 52° + 90° = 180° ?

180° = 180° ?yes

Answer 2

In this problem, we're told that the 2 smaller angles of the right triangle are (48-x) and (9x-38) degrees.

Recall that the 2 smaller angles of a right triangle add up to 90 degrees.

So we can write: (48-x) + (9x-38) = 90

Adding like terms: 8x + 10 = 90

8x = 80

x = 10

Thus the first angle is (48-x) = (48-10) = 38 degrees, and the second angle must be 90-38 = 52 degrees.

Answer 3

Hello! I would like to help you with this question!

We know that sum of angles in a triangle is 180^o.

Let's add all angles and set them to 180.

48-x+9x-38+90=180

Collect all terms:

100+8x=180

Leave x's on the left side of the equation and bring everything else on the right side.

8x=180-100

8x=80

x=10

Substitute x into your angles:

a=48-10=38^o

b=9*10-38=90-38=52^o

c=90^o

I hope it helps!