12 The opposite angles of a parallelogram PQRS are angle Q = (5x-16)° and angle S = (2x+29)°. Find all the angles of parallelogram.
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12 The opposite angles of a parallelogram PQRS are angle Q = (5x-16)° and angle S = (2x+29)°. Find all the angles of parallelogram.
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Step-by-step explanation:
ANSWER:-
Given That:-
Concept:-
Parallelograms and other 2D figures Properties
Let's Do!
First of all, we need to know that the opposite sides of Parallelogram are always equal.
The corresponding sides of a Parallelogram are supplementary of each other.
So, according to question the sides are opposite ie equal.
5x-16 = 2x+29
5x-2x = 29+16
3x = 45
[tex]\sf{x = \dfrac{45}{3}}[/tex]
x = 15°
Sp, placing the values, we get:-
5(15) - 16
= 75-16
= 59°.
So, as I said, we will find the other angles as:-
180- 59 = 121°.
Sp, 121°, 121°, 59° and 59° are the required angles.
Answer:
sum of the four angles of a parallelogram is 360°
again the opposite angles are equal.
so,
Q=(5x-16)°
S=(2x+29)°
so,
Q=S
5x-16=2x+29
=> 5x-2x=29+16
=> 3x=45
=> x=45/3=15
so, Q=(5.15-16)°=(75-16)°=59°
S=(2. 15+29)°=(30+29)°=59°
again , angle P=angle R
angle P+ angle Q+angle R+ angle S=360°
angle P+59°+angle P+59°=360°
2angleP=360°-59°-59°=242°
angle P=242/2=121°
P=121°
Q=59°
R=121°
S=59°