Question

JKLM is a square.Points P and Q are outside the square such that triangles JPM and MLQ are both equilateral. The size in degrees of angle PQM is
a)10
b)15
c)25
d)30

Answer 1

Answer:b

Step-by-step explanation:

as ∠ JPM = ∠ PMJ = ∠PJM = 60°

also ∠QML =∠ MQL = ∠ MLQ = 60°

also PM = MQ (JM =ML and ΔPJM and ΔMQL           are equilateral )

∴ In ΔPMQ,

∠PMQ = ∠MQP (angles opposite to equal sides of a Δ are equal)

Also, ∠JML + reflex∠JML= 360°

⇒reflex∠JML=270°(360-90)

Also, reflex∠JML= ∠JPM+∠PMQ+∠QML

270°=60°+∠PMQ+60°

270-120=∠PMQ

∠PMQ=150°

∴ In ΔPMQ,

∠PMQ+∠QPM+∠MQP=180°(Angle sum property of Δ)

∠PMQ+150°+∠MQP=180°

2∠PQM=180°-150°

2∠PQM=30°

∴∠PQM=30/2

∠PQM=15°