Question

In the adjoining figure side BA of triangle ABC is extended to E. Find the measure of - :
1.angle ACD
2.angle ADC
3.angle DAE​

Answer 1

Answer:

In the adjoining figure side BA of triangle ABC is extended to E. Find the measure of - :

1.angle ACD

2.angle ADC

3.angle DAE

Answer 2

ANSWER..

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1. Since, ∠ ACB and ∠ ACD makes linear pair of angles

therefore, ∠ ACB + ∠ ACD = 180°

105° + ∠ ACD = 180°

∠ ACD = 180° - 105°

∠ ACD = 75°

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2. In △ACD,

by angle sum property,

∠ CAD + ∠ ACD + ∠ ADC = 180°

60° + 75° + ∠ ADC = 180°

135° + ∠ ADC = 180°

∠ ADC = 180° - 135°

∠ ADC = 45°

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3. In △ABC,

by angle sum property,

∠ ABC + ∠ ACB + ∠ BAC = 180°

40° + 105° + ∠ BAC = 180°

145° + ∠ BAC = 180°

∠ BAC = 180° - 145°

∠ BAC = 35°

Since, ∠ BAC , ∠ CAD and ∠ DAE makes linear pair of angles

therefore, ∠ BAC + ∠ CAD + ∠ DAE = 180°

35° + 60° + ∠ DAE = 180°

∠ DAE + 95° = 180°

∠ DAE = 180° - 95°

∠ DAE = 85°

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