Question

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

Answer 1

Answer:

x = 36°

Step-by-step 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°:

$3x + mABH + x = 180$

$3x + x + x = 180$

$5x = 180$

$x = 180/5 = 36\°$