Question

PLEASE HELP (100PTS)

In the figure shown, m∠THV=(16x+20)∘, m∠THX=53∘, and m∠XHV=(12x−9)∘.

What is the value of x?

Enter your answer in the box.

Answer 1

x = 6

Explanation:

• ∠THX and ∠XHV have a common side HX and a common vertex H

This means they are two adjacent angles.

Then

m∠THX + m∠XHV = m∠THV

Then

53 + 12x−9 = 16x + 20

Solving the equation:

53 + 12x−9 = 16x + 20

⇔ (53 − 9) + 12x = 16x + 20

⇔ 44 = 16x - 12x+ 20

⇔ 44 - 20 = 4x

⇔ 24 = 4x

`\Longleftrightarrow x = (24)/(4) =6`