Question

Find the measure of each acute angle.

The measure of the top-left angle in the triangle is__º and the measure of the bottom-right angle is__º.

Answer 1

The measure of the top-left angle in the triangle is 48 ° and the measure of the bottom-right angle is 42 °.

Explanation:

We know that , the sum of angles of triangle is 180 °.

And , It is the right triangle so, bottom left is 90 °.

8 x ° + 7 x ° + 90 ° = 180 °

15 x + 90 ° = 180 ° ..( combine like terms)

Subtract each side by 90°

15 x° + 90° - 90° = 180° - 90°

15 x° = 90 °

15 x° / 15 = 90 ° / 15 ..(Divide each side by 15°)

x° = 6 °.

Using value of x to finding the

• The measure of the top left angle in the triangle is = 8 x° = 8 × 6 = 48 ° .
• The measures of the bottom right angle is = 7 x ° = 7 × 6 = 42 ° .

Answer 2

The 3 inside angles of a triangle need to equal 180 degrees.

This is a right triangle so the bottom left corner is 90 degrees.

This means the other two angles when added need to equal 180-90 = 90 degrees.

Now you have 8x + 7x = 90

Combine like terms:

15x = 90

Divide both sides by 15

X = 6

Now you have the value for x solve the two angles:

8x = 8(6) = 48

7x = 7(6) = 42

Top left = 48 degrees

Bottom right = 42 degrees