Question

Everything is in the screen shoot

Answer 1

It should be noted:

• The interior angles of a triangle sum up to 180°.

This means that:

• (180 - 142) + 68 + (180 - z) = 180

Simplify the LHS.

• 38 + 68 + (180 - z) = 180
• 106 + (180 - z) = 180

Subtract 106 both sides.

• -106 + 106 + (180 - z) = 180 - 106
• => 180 - z = 74

Subtract 180 both sides.

• => 180 - z = 74
• => 180 - 180 - z = 74 - 180
• => -z = -106

Divide both sides by -1.

• -z/-1 = -106/-1
• => z = 106

The measure of ∠z is 106°.

Answer 2

z = 106°

As a straight line has total 180°

Find the top inside angle:

t + 142° = 180°

t = 180° - 142°

t = 38°

Two opposite angles sum up to exterior angle.

Now find z:

68° + 38°

106°