Question

In the adjoining figure, ∠ ABC = 40° , ∠ ACB = 100° and ∠ CAD = 50°

Find (a) ∠ ACD (b) ∠ ADC (c) ∠ DAE

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Answer 1

Answer:

ACD = 80

ADC = 50

DAE = 90

hope it help you

Answer 2

Answer:

angle ACD = 80

angle ADC = 50

angle DEA = 90

Step-by-step explanation:

in ️ ABD,

by pair of linear angles

angle ACB + angle ACD = 180

100 + angle ACD = 180

angle ACD = 180 - 100 ------ 1

therefore , angle ACD = 80

in ️ ACD ,

by angle sum property of triangle ,

angle ACD + angle CAD + angle ADC = 180

80 + 50 + angle ADC = 180

angle ADC = 180 - 130

angle ADC = 50

in ️ ABC ,

by angle sum property of triangle

angle ABC + angle ACB + angle BAC = 180

40 + 100 + angle BAC = 180

Angle BAC = 180 - 140

angle BAC = 40 ____ 2

angle CAD = 50 ___ given

angle BAC = 40 ____ from 2

therefore angle DAB = 50 + 40 = 90

by pair of linear angle ,

angle DAB + angle DAE = 180

90 + angle DAE = 180

angle DAE = 180 - 90

Therefore, angle DAE = 90