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

Answer:

$\angle EAB = 85$

Step-by-step 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

$\angle EAB = 180-95$

$\angle EAB = 85$