Question

Ray QE is bisector of ∠PQR where ∠PQR = 75° then reflex ∠PQE =_______.

Answer 1

Answer:

Given,

∠XYZ=64

∘

YQ bisects ∠ZYP

∠XYZ+∠ZYP=180

∘

(Linear Pair)

⇒64

∘

+∠ZYP=180

∘

∠ZYP=116

∘

Also, ∠ZYP=∠ZYQ+∠QYP

∠ZYQ=∠QYP (YQ bisects∠ZYP)

⇒∠ZYP=2∠ZYQ

⇒2∠ZYQ=116

∘

⇒∠ZYQ=58

∘

=∠QYP

Now, ∠XYQ=∠XYZ+∠ZYQ

⇒∠XYQ=64

∘

+58

∘

⇒∠XYQ=122

∘

Also, reflex ∠QYP=180

∘

+∠XYQ

∠QYP=180

∘

+122

∘

⇒∠QYP=302

∘