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Find the value of x.

Find the value of x.-example-1

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Answer:

Explanation:

The angle inscribed in a semicircle is always 90°

∠ABC = 90°

In ΔABC,

∠A + ∠B + ∠C = 180

34 + 90 + ∠C = 180

124+ ∠C = 180

∠C = 180 - 124

∠C = 56°

InΔBDC, given that BD = BC

Therefore, ∠ BDC = ∠C

∠BDC = 56°

In ΔABD, external angle is equal to the sum of opposite interior angles.

∠DBA + ∠A = ∠BDC

x + 34° = 56°

x = 56° - 34°

x = 22°

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