Find the measure of - P and - S if SP - RQ- If - S is given as 90- is there any other method to find - P- 3 marks

Solution: Here, ∠ P + ∠ Q = 180^∘ [Sum of co interior angles is 180^∘] ⇒∠ P + 130^∘ = 180^∘ ⇒∠ P = nbsp;180^∘ 130^∘ ⇒∠ P = nbsp;50^∘ (1 mark) ∠ R = 9 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VII

Mathematics

Sum of Measures of Exterior Angle of a Polygon

Find the meas...

Question

Find the measure of $∠ P$ and $∠ S$ if SP || RQ.
If $∠ S$ is given as $90^{\circ}$ , is there any other method to find $∠ P$ ? (3 marks)

Open in App

Solution

Solution:

$H e r e, ∠ P + ∠ Q = 180^{\circ} [S u m o f c o - i n t e r i o r a n g l e s i s 180^{\circ}] \Rightarrow ∠ P + 130^{\circ} = 180^{\circ} \Rightarrow ∠ P = 180^{\circ} - 130^{\circ} \Rightarrow ∠ P = 50^{\circ}$
(1 mark)
$∠ R = 90^{\circ} [G i v e n] ∠ S + 90^{\circ} = 180^{\circ} [S u m o f c o - i n t e r i o r a n g l e s i s 180^{\circ}] \Rightarrow ∠ S = 180^{\circ} - 90^{\circ} \Rightarrow ∠ S = 90^{\circ}$
(1 mark)
$Y e s, w e c a n u s e a n o t h e r m e t h o d t o f i n d ∠ P ∠ S + ∠ R + ∠ Q + ∠ P = 360^{\circ} [A n g l e s u m p r o p e r t y o f q u a d r i l a t e r a l] \Rightarrow 90^{\circ} + 90^{\circ} + 130^{\circ} + ∠ P = 360^{\circ} \Rightarrow 310^{\circ} + ∠ P = 360^{\circ} \Rightarrow ∠ P = 360^{\circ} - 310^{\circ} \Rightarrow ∠ P = 50^{\circ}$ (1 mark)

Suggest Corrections

Similar questions

Q. Find the measure of

∠ P

and

∠ S

¯ ¯¯¯¯¯¯ ¯ S P ∥ ¯ ¯¯¯¯¯¯¯ ¯ R Q

& in Fig.
(If you find

m ∠ R

, is there more than one method to find

m ∠ P ?

)

Find the measure of $∠ P$ and $∠ S$ if SP || RQ. (If you find m $∠ R$ , is there more than one method to find m $∠ P$ ?

Find the measure of ∠P and ∠S, if in the following figure. (If you find m∠R, is there more than one method to find m∠P?)

Question 12
Find the measure of $∠ P$ and $∠ S$ if SP || RQ. (If you find m $∠ R$ , is there more than one method to find m $∠ P$ ?

Find the measure of $∠ P$ and $∠ S$ if SP || RQ. (If you find m $∠ R$ , is there more than one method to find m $∠ P$ ) ?

Join BYJU'S Learning Program

Find the measure of ∠P and ∠S if SP || RQ. If ∠S is given as 90∘, is there any other method to find ∠P? (3 marks)

Find the measure of $∠ P$ and $∠ S$ if SP || RQ.
If $∠ S$ is given as $90^{\circ}$ , is there any other method to find $∠ P$ ? (3 marks)