the adjoining figure, if AB = PQ and BC = CQ, then find the measure of angle CPQ.
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To find:
- Measure of angle CPQ
Solution:
<QCP=30° [Vertically opposite angles]
As we know,
Angle sum property of the traingle
Angle CPQ(X)=80°
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Answer:
The measure of ∠CPQ is 80°.
Step-by-step explanation:
It is given that in the adjoining figure, AB = PQ and BC = CQ.
To find the measure of angle CPQ, i.e., ∠CPQ =?
From the figure,
Notice that the line segments AP and BQ intersect each other at a point C.
This implies, the opposite angles are equal.
⇒ ∠PCQ = ∠BCA (Vertically opposite angles)
⇒ ∠PCQ = 30° (From figure, ∠BCA = 30°)
Now,
In Δ PCQ,
∠CQP + ∠PCQ + ∠CPQ = 180° (Angle sum property)
70° + 30° + ∠CPQ = 180°
100° + ∠CPQ = 180°
∠CPQ = 180° - 100°
∠CPQ = 80°
Therefore, the measure of ∠CPQ is 80°.
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