Question

ADC is a triangle.

AED and ABC are straight lines.

EB is parallel to DC.

Angle EBC=148°

Angle ADC=63°

Work out the size of angle EAB.

You must give a reason for each stage of your working out.

Answer 1

`\angle EAB = 85`

Explanation:

Given

`\angle EBC = 148`

`\angle ADC = 63`

See attachment for triangle

Required

Find EAB

`\angle AEB = \angle ADC = 63` --- corresponding angles

`\angle ABE + \angle EBC = 180` --- angle on a straight line

So:

`\angle ABE + 148 = 180`

This gives:

`\angle ABE =- 148 + 180`

`\angle ABE =32`

Considering:
`\triangle ABE`

`\angle ABE +\angle AEB +\angle EAB = 180` --- angles ina triangle

So:

`32 +63+\angle EAB = 180`

`95+\angle EAB = 180`

Collect like terms

`\angle EAB = 180-95`

`\angle EAB = 85`