Name: Trapezium and Its Properties
Uploaded: 2019-07-19
Duration: 3 min 54 s
Description: A trapezium is a special convex quadrilateral having only one pair of opposite sides parallel. This video explains the diagrammatic representation of a trape...

Question

In the adjacent figure, the bisectors of $∠ A$ and $∠ B$ meet in a point $P$ . If $∠ C = 100 °$ and $∠ D = 60 °$ , find the measure of $∠ A P B$ .

Accepted Answer

Given that the bisectors of $∠ A$ and $∠ B$ meet in a point $P$ .

$∠ C = 100 °$ and $∠ D = 60 °$

We are asked to find the measure of $∠ A P B$ .

We know that the sum of angles of a quadrilateral is $360 °$ .

$\Rightarrow ∠ A + ∠ B + ∠ C + ∠ D = 360 °$

$\Rightarrow ∠ A + ∠ B + 100 ° + 60 ° = 360 °$

$\Rightarrow ∠ A + ∠ B = 360 ° - (100 ° + 60 °)$

$\Rightarrow ∠ A + ∠ B = 360 ° - 160 °$

$\Rightarrow ∠ A + ∠ B = 200 °$

$A P & B P$ are the angle bisectors of $∠ A & ∠ B$ respectively.

$\Rightarrow ∠ P A B = ∠ P A D = \frac{1}{2} ∠ A$ and

$∠ A B P = ∠ P B C = \frac{1}{2} ∠ B$

Now consider $△ A P B$ .

We know that the sum of the angles of a triangle is $180 °$ .

$\Rightarrow ∠ P A B + ∠ P B A + ∠ A P B = 180 °$

$\Rightarrow \frac{1}{2} ∠ A + \frac{1}{2} ∠ B + ∠ A P B = 180 °$

$\Rightarrow \frac{1}{2} (∠ A + ∠ B) + ∠ A P B = 180 °$

$\Rightarrow \frac{1}{2} \times 200 ° + ∠ A P B = 180 °$

$\Rightarrow 100 ° + ∠ A P B = 180 °$

$\Rightarrow ∠ A P B = 180 ° - 100 °$

$\Rightarrow ∠ A P B = 80 °$

Hence, the measure of $∠ A P B$ is $80 °$ .

In the adjacent figure, the bisectors of $∠ A$ and $∠ B$ meet in a point $P$ . If $∠ C = 100 °$ and $∠ D = 60 °$ , find the measure of $∠ A P B$ .

Important Questions on Quadrilaterals

Learn and Prepare for any exam you want !

In the adjacent figure, the bisectors of ∠A and ∠B meet in a point P. If ∠C=100° and ∠D=60°, find the measure of ∠APB.

Important Questions on Quadrilaterals

Learn and Prepare for any exam you want !

In the adjacent figure, the bisectors of $∠ A$ and $∠ B$ meet in a point $P$ . If $∠ C = 100 °$ and $∠ D = 60 °$ , find the measure of $∠ A P B$ .