Answer:

First picture:

x + 2x + 30° = 90°

x + 2x = 90° - 30°

3x = 60°

x = 20°

ABD = 2x = 2(20°) = 40°

Second picture:

m∠1 = m∠3

m∠3 = 35°

ABE = m∠1 + m∠2

90° = m∠1 + 42°

m∠1 = 90° - 42°

m∠1 = 48°

m∠1 = m∠3

m∠3 = 48°

Third picture:

(2x - 10) + (x + 4) = 90

2x + x = 90 + 10 - 4

3x = 96

x = 32

m∠ABD = 2x - 10

m∠ABD = 2(32) - 10

m∠ABD = 54°

m∠CBD = x + 4

m∠CBD = 32 + 4

m∠CBD = 36°

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