YourAverageFangirl
YourAverageFangirl YourAverageFangirl
  • 25-09-2020
  • Mathematics
contestada

Given:△ABC∼△DEF, ∠C is a right angle, AB=17, AC=15, BC=8, m∠B=62∘, DE=34, EF=16,and DF=30.


What is the measure of ∠D?

GivenABCDEF C is a right angle AB17 AC15 BC8 mB62 DE34 EF16and DF30What is the measure of D class=

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mhanifa
mhanifa mhanifa
  • 25-09-2020

Answer:

  • 28°

Step-by-step explanation:

We can see the scale factor is 2 from the side lengths:

  • 8→16, 15→30, 17→34

Corresponding sides are:

  • AB and DE
  • AC and DF
  • BC and EF

Corresponding angles are opposite to corresponding sides:

  • ∠C≅∠F
  • ∠A≅∠D
  • ∠B≅∠E

So

  • m∠A = 90° - 62° = 28°

Therefore

  • m∠D = 28°
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