Question

12 The opposite angles of a parallelogram PQRS are angle Q = (5x-16)° and angle S = (2x+29)°. Find all the angles of parallelogram.

Answer 1

Step-by-step explanation:

ANSWER:-

Given That:-

• The opposite sides of a Parallelogram is 5x-16 and 2x+29
• The given condition is that it is a Parallelogram

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

$\sf{x = \dfrac{45}{3}}$

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 2

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°