In the figure given alongside find angle acd, angle adc, angle dae

Answers
Angle ACB + Angle ACD = 180° (Linear Pair)
= 100 + ACD = 180
= Angle ACD = 80°
Angle ADC = 180 - (ACD + CAD)
[ASP of triangle]
= 180 - (80 + 50) = 180 - 130 = 50°
Angle BAC = 40° (Using ASP triangle)
Angle DAE = 180 - (DAC + BAC)
= 180 - (50 + 40) = 180 - 90 = 90°
∠ACD = 80°, ∠ADC = 50° and ∠DAE = 90°
Given: From given figure In triangle ABC
∠ABC = 40° and ∠ ACB = 100° and ∠CAD = 50°
To find: The measures of ∠ ACD, ∠ ADC, ∠ DAE
Solution: From given figure,
⇒ ∠ ACB + ∠ ACD = 180° [ ∵ ∠ACB, ∠ACD are Linear pair ]
⇒ 100° + ∠ ACD = 180° [ ∵ ∠ ACB = 100° ]
⇒ ∠ ACD = 180° - 100° = 80°
Therefore, ∠ACD = 80°
As we know sum of angles in a triangle = 180°
From Triangle, ACD
⇒ ∠ ACD + ∠ ADC +∠CAD = 180°
⇒ 80°+ ∠ADC + 50° = 180°
⇒ ∠ADC + 130° = 180°
⇒ ∠ADC = 180° - 130° = 50°
Therefore, ∠ADC = 50°
From triangle ABC
⇒ ∠ABC + ∠BCA + ∠BAC = 180°
⇒ 40° + 100° + ∠CAB = 180°
⇒ ∠BAC + 140° = 180°
⇒ ∠BAC = 40°
From figure, ∠BAC + ∠CAD + ∠DAE = 180° [ BAE is a straight line ]
⇒ 40° + 50° + ∠DAE = 180°
⇒ ∠DAE + 90° = 180°
⇒ ∠DAE = 180° - 90° = 90°
Therefore, ∠DAE = 90°
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