Answer:
1) x = 8
2) ∠RPS = 36°
Step-by-step explanation:
GIVEN :-
- ∠QPS = 180°
- ∠QPR = 7x + 88
- ∠RPS = 3x + 12
TO FIND :-
- Value of x
- Measure of ∠RPS
FACTS TO KNOW BEFORE SOLVING :-
In a straight line , if there are two angles such that their sum is equal to straight angle (or 180° in other words) , then those angles are known as linear pair.
PROCEDURE :-
1)
Measure of ∠QPS = 180° and it comprises of ∠QPR & ∠RPS.
⇒ ∠QPR & ∠RPS are linear pair.
⇒ ∠QPR + ∠RPS = 180°
⇒ 7x + 88 + 3x + 12 = 180°
⇒ 10x + 100 = 180
⇒ 10x = 180 - 100 = 80
⇒ x = 80/10 = 8
2)
x = 8. So,
∠RPS = 3×8 + 12 = 24 + 12 = 36°
