the bisectors of exterior angles Q and R of triangle PQR meet at O. if angle QPR is 40 degree, then the measure of angle QOR is
Answers
Answer:
I think the answer is 70 degrees. I am not sure about my answer.
Step-by-step explanation:
x+x+x=180
2x+40=180
2x=180-40
2x=140
x=140by2
x=70 degrees
Given : the bisectors of exterior angles Q and R of triangle PQR meet at O. Angle QPR is 40 degree,
To Find : the measure of angle QOR
Solution:
Concepts to be used:
Sum of angles of a triangle is 180°
Exterior angle of triangle = Sum of opposite two interior angles
Angle bisector Divides the angle in two half
in Δ QOR
∠RQO + ∠QRO + ∠QOR = 180°
=> (1/2) (exterior angles Q) + (1/2) (exterior angles R) + ∠QOR = 180°
exterior angles Q = ∠P + ∠R
exterior angles R = ∠P + ∠Q
=> (1/2) (∠P + ∠R) + (1/2) (∠P + ∠Q) + ∠QOR = 180°
=> (1/2) ( ∠P + ∠R + ∠P + ∠Q) + ∠QOR = 180°
=>(1/2) ( ∠P + ∠P + ∠Q + ∠R) + ∠QOR = 180°
∠P + ∠Q + ∠R = 180°
∠P = 40°
=> (1/2) ( 40° + 180°) + ∠QOR = 180°
=>110° + ∠QOR = 180°
=> ∠QOR =70°
Hence measure of angle QOR is 70°
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