Name: Angles of a Polygon
Uploaded: 2019-07-19
Duration: 18 min 4 s
Description: This video will take you through everything you need to know about the angles of polygons. It focusses on convex regular polygons. Watch the video to learn m...

Question

Lines $A C$ and $B D$ intersect at point $P$ and $m ∠ A P D = 47 °$ . Find the measures of $∠ A P B$ , $∠ B P C$ and $∠ C P D$ .

Accepted Answer

Given,

Lines $A C$ and $B D$ intersect at $P$ and $m ∠ A P D = 47 °$ .

We know that,

Vertically opposite angles are formed when two lines intersect and they are of equal measure.

Also, linear pair of angles are supplementary angles.

Let $∠ C P D$

From the given figure, we can conclude that

$a$ and $c$ are vertically opposite angles.

Therefore, $a = c = 47 °$

Angles $a$ and $b$ form a linear pair.

$\Rightarrow a + b = 180 °$

$\Rightarrow 47 ° + b = 180 °$

$\Rightarrow b = 180 ° - 47 °$

$\Rightarrow b = 133 °$

Now, $b$ and $d$ are vertically opposite angles.

Hence, $b = d = 133 °$

Therefore, $∠ A P B = 133 °$ , $∠ B P C = 47 °$ and $∠ C P D = 133 °$ .

Maharashtra Board Solutions for Exercise 6: Practice Set 20

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Exercise 6: Practice Set 20

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