In the figure PQ perpendicular to PR, angleRQE=38degree, angleQTL=75degree find x and y.
Answers
Given : PQ perpendicular to PR, PQ parallel RL, Angle RQT = 38 degree and Angle QTL = 75 degree
To Find : X and Y .
Solution:
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Interior angles are supplementary. ( adds up to 180°)
PQ || RL
QT is transversal
∠PQT = ∠QTL ( alternate interior angles)
∠PQT = y + 38°
Hence y + 38° = 75°
=> y = 37°
PQ || RL
QR is transversal
∠PQR = ∠QRT
=> y = ∠QRT
=> ∠QRT = 37°
PQ || RL
PR is transversal
∠QPR + ∠PRT = 180° Interior angles adds upto 180°
∠PRT = x + ∠QRT
∠QPR = 90°
=> 90° + x + 37° = 180°
=> x = 53°
x = 53°
y = 37°
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