Question

Label the vertices and all the elements needed. find x. give reasons!

Answer 1

`x = 36^o`

Explanation:

Given

See attachment

Required

Find x

First, calculate
`\angle BAH`

`\angle BAH + 90 + x = 180` --- angle on a straight line

Collect like terms

`\angle BAH = 180 -90-x`

`\angle BAH = 90-x`

Next, calculate
`\angle HBA`

`\angle HBA + x + 3x = 180` --- angle on a straight line

`\angle HBA + 4x = 180`

Rewrite as:

`\angle HBA = 180-4x`

`\triangle HBA` is right-angled;

So:

`\angle HBA + \angle BAH + 90 = 180`

This gives:

`180 - 4x + 90 - x+ 90 = 180`

Collect like terms

`- 4x - x = 180 - 180 - 90 - 90`

`- 5x = -180`

Divide both sides by -5

`x = 36^o`