Question

the adjoining figure, if AB = PQ and BC = CQ, then find the measure of angle CPQ.​

Answer 1

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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

$\begin{gathered}\qquad \longmapsto \cal{{\red{ <A+<B+<C=180° }} } \\\end{gathered} \\ \\ \begin{gathered}\qquad \longmapsto \frak{{ 70 + 30 + x = 180 } } \\\end{gathered} \\ \\ \begin{gathered}\qquad \longmapsto \frak{{ 100 + x = 180 } } \\\end{gathered} \\ \\ \begin{gathered}\qquad \longmapsto \frak{{ x = 180 - 100 } } \\\end{gathered} \\ \\ \begin{gathered}\qquad \longmapsto \frak{{ x = 80 } } \\\end{gathered}$

Angle CPQ(X)=80°

$\: \: \: \: \: \: \: \: \: \: \huge \bold{@WildCat7083 }$

Answer 2

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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