Question

Label the vertices and all the elements needed. Find x. Give reasons!

Answer 1

x = 36°

Explanation:

Please check the labels in the image attached.

In vertex A, the sum of the angles in the line AB is 180°, so we have:

`x + 90 + mA = 180`

`mA = 90 - x`

The angle mCHB is a right angle, so the angle mAHB is also a right angle.

Then, using the internal angles of triangle AHB, we have:

`mA + mAHB + mABH = 180`

`90 - x + 90 + mABH = 180`

`mABH = x`

Then, in vertex B, we have the sum of angles in the line BC equal to 180°:

`3x + mABH + x = 180`

`3x + x + x = 180`

`5x = 180`

`x = 180/5 = 36\°`