Q.12 The opposite angles of a parallelogram PQRS are angle Q = (5x-16)

1.	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» 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.

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»

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

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,