In the given figure, AB || CD. If ∠APQ = 70° and ∠PRD = 120°, then ∠QPR = ?
(a) 50°
(b) 60°
(c) 40°
(d) 35°

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Solution

(a) 50°

$A B ∥ C D and P Q$ is the transversal.
$∴ ∠ P Q R = ∠ A P Q = 70 ° [Alternate Interior Angles]$
Side QR of traingle PQR is produced to D.
$∴ ∠ P Q R + ∠ Q P R = ∠ P R D \Rightarrow 70 ° + ∠ Q P R = 120 ° \Rightarrow ∠ Q P R = 50 °$

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Similar questions

In the given figure, AB||CD. If $∠ A P Q = 70^{\circ}$ and $∠ P R D = 120^{\circ}$ then $∠ Q P R = ?$

$(a) 50^{\circ}$

$(b) 60^{\circ}$

$(c) 40^{\circ}$

$(d) 35^{\circ}$

Q. In the given figure

A B ∥ C D, ∠ A P Q = 50^{\circ}

and

∠ P R D = 120^{\circ}

. Find

∠ Q P R

Q. In the given figure, if

A B | | C D, ∠ A P Q = 50^{\circ} a n d ∠ P R D = 127^{\circ}

, the value of y is:

In the figure if AB ||CD, ∠APQ = 50^o and ∠PRD = 127^o then y is equal to

Question 10
In the given figure, If $A B | | C D, ∠ A P Q = 50^{\circ} a n d ∠ P R D = 130^{\circ},$ then

(a) $130^{\circ}$
(b) $50^{\circ}$
(c) $80^{\circ}$
(d) $30^{\circ}$

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In the given figure, AB || CD. If ∠APQ = 70° and ∠PRD = 120°, then ∠QPR = ? (a) 50° (b) 60° (c) 40° (d) 35°

(a) 50° AB∥CD and PQ is the transversal. ∴∠PQR=∠APQ=70° Alternate Interior Angles Side QR of traingle PQR is produced to D. ∴∠PQR+∠QPR=∠PRD⇒70°+∠QPR=120°⇒∠QPR=50°

In the given figure, AB || CD. If ∠APQ = 70° and ∠PRD = 120°, then ∠QPR = ?
(a) 50°
(b) 60°
(c) 40°
(d) 35°

(a) 50°

$A B ∥ C D and P Q$ is the transversal.
$∴ ∠ P Q R = ∠ A P Q = 70 ° [Alternate Interior Angles]$
Side QR of traingle PQR is produced to D.
$∴ ∠ P Q R + ∠ Q P R = ∠ P R D \Rightarrow 70 ° + ∠ Q P R = 120 ° \Rightarrow ∠ Q P R = 50 °$