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:

[tex]\angle EAB = 85[/tex]

Step-by-step explanation:

Given

[tex]\angle EBC = 148[/tex]

[tex]\angle ADC = 63[/tex]

See attachment for triangle

Required

Find EAB

[tex]\angle AEB = \angle ADC = 63[/tex]  --- corresponding angles

[tex]\angle ABE + \angle EBC = 180[/tex] --- angle on a straight line

So:

[tex]\angle ABE + 148 = 180[/tex]

This gives:

[tex]\angle ABE =- 148 + 180[/tex]

[tex]\angle ABE =32[/tex]

Considering: [tex]\triangle ABE[/tex]

[tex]\angle ABE +\angle AEB +\angle EAB = 180[/tex] --- angles ina triangle

So:

[tex]32 +63+\angle EAB = 180[/tex]

[tex]95+\angle EAB = 180[/tex]

Collect like terms

[tex]\angle EAB = 180-95[/tex]

[tex]\angle EAB = 85[/tex]

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