Line AB is parallel to line CD. A transversal line EF intersects line AB at point P and li… — JAMB UTME

Line $AB$ is parallel to line $CD$ . A transversal line $EF$ intersects line $AB$ at point $P$ and line $CD$ at point $Q$ . If $\angle APQ = (4x - 10)^\circ$ and $\angle PQD = (2x + 30)^\circ$ are alternate interior angles, what is the measure of $\angle BPQ$ ?

$110^\circ$ Cevap
B
$70^\circ$
C
$20^\circ$
D
$100^\circ$

Cevap

110^\circ

Since alternate interior angles are equal,

4x - 10 = 2x + 30

, yielding

x = 20

. Thus,

\angle APQ = 70^\circ

. Because

\angle APQ

and

\angle BPQ

are adjacent angles on straight line

AB

, their sum is

180^\circ

, giving

\angle BPQ = 110^\circ

Adım Adım Çözüm

Set up the equation for alternate interior angles.

4x - 10 = 2x + 30

Alternate interior angles formed by a transversal cutting parallel lines are equal.

Solve the linear equation for

x

2x = 40 \implies x = 20

Subtract

2x

and add

10

to both sides.

Calculate the measure of

\angle APQ

\angle APQ = 4(20) - 10 = 70^\circ$

Substitute

x = 20

into the expression

(4x - 10)^\circ

Determine

\angle BPQ

using the straight line angle property.

\angle BPQ = 180^\circ - 70^\circ = 110^\circ$

Angles

\angle APQ

and

\angle BPQ

form a linear pair on straight line

AB

, summing to

180^\circ

Anahtar Kavram

Alternate interior angles of parallel lines and angles on a straight line

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru