Class 8 Maths Exercise 3.3 Question 12 Solution

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

Solution:

$[ \angle P + \angle Q = 180° ]$ {Angles on the same side of transversal}

$[ \Rightarrow \angle P + 130° = 180° ]$

$[ \Rightarrow \angle P = 180° – 130° = 50° ]$

Also,

$[ \angle R + \angle S = 180° ]$ {Angles on the same side of transversal}

$[ \Rightarrow 90° + \angle S = 180° ]$

$[ \Rightarrow \angle S = 180° – 90° = 90° ]$

Hence, $( \angle P = 50° )$ and $( \angle S = 90° )$

Yes, there is more than one method to find $(m\angle P)$.

Since PQRS is a quadrilateral, the sum of the measures of all angles of a quadrilateral is (360°).

Thus, as we know the measurements of $( \angle Q)$, $( \angle R)$, and $( \angle S)$:

$[ \angle Q = 130°, \angle R = 90°, \text{ and } \angle S = 90° ]$

$[ \angle P + 130° + 90° + 90° = 360° ]$

$[ \Rightarrow \angle P + 310° = 360° ]$

$[ \Rightarrow \angle P = 360° – 310° = 50° ]$