Maths-
General
Easy

Question


Triangle DEF (not shown) is similar to triangle ABC above, where side DE corresponds to side AB, side DF corresponds to side AC , and DE = AB. What is the measure of angle DEF ?

  1. 37 to the power of ring operator
  2. 53 to the power of ring operator
  3. 74 to the power of ring operator
  4. 106 to the power of ring operator

The correct answer is: 53 to the power of ring operator


    HINT : In similar triangles the corresponding angles will be equal in the same order of the similarity.
    Explanation: Given ΔDEF is similar to ΔABC
    Step 1: Check the similarity order
    Side DE corresponds to AB (ΔDEF ~ ΔABC)
    Side DF corresponds to AC (ΔDEF ~ ΔABC)
    Verified successfully that ΔDEF ~ ΔABC are in correct order of similarity then
    Step 2:Finding all angles of  ΔABC
    In  ΔABC ,∠A = 90° ,∠B = 37°(given in diagram)
    But ∠A +∠B +∠C = 180°( sum of angles in a triangle )
    90° +  37°+∠C =180°
    ∠C =180°-  90° - 37°
    ∴∠C =53°=∠ACB
    Step 3:
    ∠DFE = ∠ACB (By similarity of triangles)
    ∠DFE=∠ACB= 53°
    ∴∠DFE = 53°

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