Question

Lines AC and BD intersect at point P. measure angle APD = 47° Find the measures of angle APB, angle BPC, angle CPD
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Answer 1

Answer:

Step-by-step explanation:

∠APD = 47°

∠APD  =  ∠BPC = 47° { vertically opposite angles }

∠APB + ∠APD =  180° { angles in a straight line}

∠APB + 47° = 180°

∠APB = 133° = ∠CPD { vertically opposite angles }

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Answer 2

Given,

Lines AC and BD intersect at P,

∠APD = 47°.

To find,

∠APB, ∠BPC, and ∠CPD.

Solution,

Here, the two lines AC and BD are given to be intersecting at a point P. Also, the ∠APD is 47°.

Now, it can be seen that, as AC intersects with BD at P, the angles will form some specific pairs, and thus, the required angles can be determined as follows.

∠APB and ∠APD = Linear pair

Since sum of angles forming a linear pair is equal to 180°.

⇒ ∠APB + ∠APD = 180

⇒ ∠APB = 180 - ∠APD

⇒ ∠APB = 180 - 47

⇒ ∠APB = 133°.

∠BPC and ∠APD = Vertically opposite angles

Since vertically opposite angles are equal.

⇒ ∠BPC = ∠APD

⇒ ∠BPC = 47°.

∠CPD and ∠APD = Linear pair

⇒ ∠CPD + ∠APD = 180,

⇒ ∠CPD = 180 - ∠APD

⇒ ∠CPD = 180 - 47

⇒ ∠CPD = 133°.

Also, ∠CPD and ∠APB are vertically opposite angles.

⇒ ∠CPD = ∠APB = 133°.

Therefore, for the given lines AC and BD intersecting at P, ∠APB = 133°, ∠BPC = 47°, ∠CPD = 133°.