Name: Types of Quadrilaterals and Other Polygons
Uploaded: 2019-07-19
Duration: 8 min 41 s
Description: Four points can either form a rhombus, a square, or a rectangle. Can we find out which one it is? Watch to find out the answer for yourself!!

Question

$SNAP$ is a parallelogram in which $∠ PSO = 50 °$ and $∠ NSO = 25 °$ and $∠ AOP = 60 °$ . Find $∠ SNO, ∠ OPA, ∠ SAN$ and $∠ ANP$ .

Accepted Answer

Given, $S N A P$ is a parallelogram and $∠ NSO = 25 °$

$∠ P S N = 75 °$

We know that, the opposite angles of a parallelogram are equal.

$\Rightarrow ∠ P A N = 75 º$

We can say that $∠ S O N = ∠ A O P = 60 º$ (Vertically Opposite angles are equal)

We know that, in a parallelogram the opposite sides are parallel, then using alternate interior angle theorem,

Then, $∠ P S O = ∠ S A N = 50 º$

So $∠ S A N = 50 º$

In $∆ S O N$ ,

Using angle sum property,

$∠ S O N + ∠ O N S + ∠ N S O = 180 º$

$60 º + ∠ O N S + 25 º = 180 º$

$\Rightarrow ∠ O N S = 95 º$

$∠ ANP$ (Linear pair)

$∠ A O N =$ $180 ° - 60 ° = 120 °$

$∠ A O N + ∠ O N A + ∠ N A O = 180 º$

$120 º + ∠ O N A + 50 º = 180 º$

$∠ O N A = 10 º$

Since $P S ∥ A N$ , then using alternate interior angle theorem,

Then $∠ O P S = 10 º$

and also, $∠ O P A = ∠ O N S = 95 º$

$\Rightarrow ∠ O P A = 95 º$

$∠ A N P = ∠ O N A = 10 º$

$\Rightarrow ∠ A N P = 10 º$

Hence, $∠ S N O = 95 °, ∠ O P A = 95 °, ∠ S A N = 50 °, ∠ A N P = 10 °$

$SNAP$ is a parallelogram in which $∠ PSO = 50 °$ and $∠ NSO = 25 °$ and $∠ AOP = 60 °$ . Find $∠ SNO, ∠ OPA, ∠ SAN$ and $∠ ANP$ .

Important Questions on Understanding Quadrilaterals

Learn and Prepare for any exam you want !

SNAP is a parallelogram in which ∠PSO=50° and ∠NSO=25° and ∠AOP=60°. Find ∠SNO,∠OPA,∠SAN and ∠ANP.

Important Questions on Understanding Quadrilaterals

Learn and Prepare for any exam you want !

$SNAP$ is a parallelogram in which $∠ PSO = 50 °$ and $∠ NSO = 25 °$ and $∠ AOP = 60 °$ . Find $∠ SNO, ∠ OPA, ∠ SAN$ and $∠ ANP$ .