Q11 of 32 Page 60

In figure 5.38 if PQ || RS, ∠MXQ° = 135° and ∠MYR = 40°, then find ∠XMY.

Given:


PQ || RS, ∠MXQ° = 135° and ∠MYR = 40°


Construction:


Draw a line parallel to both PQ and RS from point M


Theory:


⇒ If 2 lines are parallel then their corresponding angles are equal


⇒ If 2 lines are parallel then sum of their internal angles is 180°


As the constructed line is parallel to RS


By alternate interior angle


The lower part of ∠ M = 40°


As the constructed line is parallel to PQ


By internal angle


Upper part of ∠ M + ∠ MXY = 180°


Upper part of ∠ M = 180° - 135° = 45°


Adding both we get


∠ XMY = 45° + 40° = 85°


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