Mathematics
Grade9
Easy

Question

If ∆UDE ~ ∆UTS, then find the measure of angle U T S.

  1. 30°
  2. 70°
  3. 60°
  4. 50°

hintHint:

The similarity of triangles can be defined based on their properties. Two triangles are similar, if
(i) their corresponding angles are equal and
(ii) their corresponding sides are in the same ratio (or proportion).
These two are the main conditions for the similarity of triangles.

The correct answer is: 70°



    In, ∆UDE
    angleU + angleE + angleD = 180degree ( By angle sum property)
    angleD = 70degree
    Since, ∆UDE ~ ∆UTS
    angleD = angleT = 70degree
    Thus,  the measure of angle U T S is 70degree.

    In similar triangles angles are congruent
    By angle sum property 180 - (80 + 30) = 70°.

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