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Question

# Find the measure of ∠ADC in the given figure.

A

30

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B

45

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C

60

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D

75

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Solution

## The correct option is C 60∘ In △ABD, ∠DAB+∠BDA+∠ABD=180∘ (Sum of all the interior angles of a triangle is 180∘) ⇒∠BDA=180∘−∠DAB−∠ABD⇒∠BDA=180∘−60∘−90∘⇒∠BDA=30∘ Since BC = CD, △BCD is an isosceles triangle. ∴ ∠CBD=∠CDB (Angles opposite to equal sides are equal) In △BCD, ∠BCD+∠CBD+∠CDB=180∘ (Sum of all the interior angles of a triangle is 180∘) ⇒∠BCD+2×∠CDB=180∘ ⇒120∘+2×∠CDB=180∘ ⇒∠CDB = 180∘−120∘2 ⇒∠CDB=30∘ From the figure, we know that, ∠ADC=∠ADB+∠CDB ⇒∠ADC=30∘+30∘ ⇒∠ADC=60∘

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