Question

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Answer 1

y = 90°

Solution:

The reference image for the answer is attached below.

The sum of opposite interior angles is equal to the exterior angles.

m∠BAC + m∠ACB = 110°

m∠BAC + 70° = 110°

m∠BAC = 110° –  70°

m∠BAC = 40°

m∠BAD + m∠DAC = 40°

x + x = 40°

2x = 40°

Divide by 2 on both sides of the equation.

x = 20°

In triangle DAC,

Sum of all the angles of a triangle = 180°

m∠DAC + m∠ACD + m∠CDA = 180°

20° + 70° + m∠CDA = 180°

90° + m∠CDA = 180°

m∠CDA = 180° – 90°

m∠CDA = 90°

∠CDA and y lies on the straight line. So they form a linear pair.

y + m∠CDA = 180°

y + 90° = 180°

y = 180° – 90°

y = 90°

The value of y is 90°.