Question

Q.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

Given:

• The opposite angles of a Parallelogram is (5x-16)° and (2x+29)°

To Find:

• Find all the angles of parallelogram.

Solution:

${\underbrace{\tt\large{ Understanding \ the \ Concept }}}$

• The opposite sides of Parallelogram are always equal.
• The corresponding sides of a Parallelogram are supplementary of each other.

So,

The sides are opposite ie equal.

$\colon\implies$ 5x - 16 = 2x + 29

$\colon\implies$ 5x - 2x = 29 + 16

$\colon\implies$3x = 45

$\colon\implies{\tt{ x = \cancel{ \dfrac{45}{3} } }}$

$\colon\implies$ x = 15°

So, After substituting values,

$\implies$ 5(15) - 16

$\implies$ 75-16

$\implies$ 59°

So, In this way we can find the Other Angles of the Parallelogram:

180 - 59 = 121°

Hence,

• 121°, 121°, 59° and 59° are the angles of Parallelogram.