Question

In the given figure, XY||AB. Find the value of reflex angle of PMQ.​

Answer 1

Given

• XY||AB
• YPM=130°
• AQM=50°

To Find

• Reflex Angle Of PMQ

Construction

• Through point m draw a line MC parallel to AB and XY

Now,

CM||AQ Construction

→∠AQM+∠CMQ =180° Co Interior Angles

→50°+∠CMQ=180°

→∠CMQ=180°-50°

∠CMQ=130°

It Is Given That AB || XY And CM||AQ by Construction Therefore,

XY||CM [LINES PARALLEL TO THE SAME LINES ARE PARALLEL TO EACH OTHER]

→∠YPM=∠CMP Alternate Angles

∠CMP=130°

Now

→Reflex ∠PMQ= ∠CMP+∠CMQ

→Reflex ∠PMQ= 130°+130°

Reflex ∠PMQ= 260°