In the diagram, |SR| = |QR|. < SRP = 65° and < RPQ = 48°, find < PRQ
Question
In the diagram, |SR| = |QR|. < SRP = 65° and < RPQ = 48°, find < PRQ
Options
A)
65°
B)
45°
C)
25°
D)
19°
The correct answer is D.
Explanation:
< RSQ = < RPQ = 48° (angle in the same segment)
< SQR < RSQ (Base angle of an isosceles Δ)
< SQR = 48°
< QRS + < RSQ + < RSQ = 180°(sum of interior angles of a Δ)
i.e. < QRS + 48° + 48° = 180°
< QRS = 180 - (48 + 48) = 180 - 96 = 84°
but < PRQ + < PRS = < QRS
< PRQ = < QRS - < PRS - 84 - 65
= 19°
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< RSQ = < RPQ = 48° (angle in the same segment)
< SQR < RSQ (Base angle of an isosceles Δ)
< SQR = 48°
< QRS + < RSQ + < RSQ = 180°(sum of interior angles of a Δ)
i.e. < QRS + 48° + 48° = 180°
< QRS = 180 - (48 + 48) = 180 - 96 = 84°
but < PRQ + < PRS = < QRS
< PRQ = < QRS - < PRS - 84 - 65
= 19°