Question

if pq is parallel to pr, qp || rl, angle rqt=38' and angle qtl=75' , find angle prq and angle pqr in the figure given below;​

Answer 1

Answer:

Acc. exterior angle property,

38°+angle QRT = 75°

angleQRT = 37

As PQ||RL ,

angle PQR = 37°

Acc. angle sum property in triangle PQR ,

90°+37°+anglePRQ = 180°

=> anglePRQ= 53°

anglePRQ = 53° and angleQRT = 37°

Hope this answer helps you out.

Answer 2

Answer:

GIVEN :-

PQ ⟂ PR.

PQ || RL.

∠RQT = 38°.

∠QTL = 75°.

TO FIND :-

The value of x and y.

SOLUTION :-

➳ ∠QTL + ∠QTR = 180°. [ Linear Pair ]

➳ 75° + ∠QTR = 180°

➳ ∠QTR = 180° - 75°

➳ ∠QTR = 105°.

✮ In ∆ QRT By angle sum property,

➠ ∠RQT + ∠QRT + ∠QTR = 180°

➠ ∠QRT + 38° + 105° = 180°

➠ ∠QRT + 143° = 180°

➠ ∠QRT = 180° - 143°

➠ ∠QRT = 37°

✭ Value of x,

➳ ∠P + ∠R = 180°. [ Allied angles ]

➳ 90° + ∠QRT + x = 180°

➳ 90° + 37° + x = 180°

➳ 127° + x = 180°

➳ x = 180° - 127°

➳ x = 53°

✭ Value of y,

➠ ∠RPQ + ∠PRQ + ∠PQR = 180°

➠ 90° + 53° + y = 180°

➠ y = 180° - 143

➠ y = 37°.