Question

PORS is a parallelogram with PQ || SR. If angleP = (2x+10)°and angleQ = (3x – 25), find the value of x and the
measures of all the angles of parallelogram PQRS.​​

Answer 1

$\bigstar$ Question:

• PORS is a parallelogram with PQ || SR. If $\angle$P = (2x+10)° and $\angle$Q = (3x – 25), find the value of x and the measures of all the angles of parallelogram PQRS.

$\bigstar$ Given:

• $\angle$ P = (2x + 10°)
• $\angle$ Q = (3x - 25°)

$\bigstar$To find:

• The value of x and the measures of all angles in that parallelogram.

$\bigstar$ Solution:

$\because$we know that the sum of the adjacent angles in a parallelogram is 180°,

$\therefore$ (2x + 10°) + (3x - 25°) = 180°

$\implies$ 2x + 3x + 10° - 25° = 180°

$\implies$ 5x - 15° = 180°

$\implies$ 5x = 180° + 15°

$\implies$ 5x = 195°

$\implies$ x = 195°/5

$\implies$ x = 39°

So, the value of x is 39°.

And the measures of all angles :

$\angle$ P

= (2x + 10°)

= (2 × 39 + 10)

= 88°

$\angle$ Q

= (3x - 25° )

= (3 × 39 - 25)

= 92°

$\angle$ R = $\angle$P = 88°

( Since opposite angles in a parallelogram are equal)

$\angle$ S = $\angle$ Q = 92°

( Since opposite angles in a parallelogram are equal)

$\bigstar$ Answer:

• Therefore, the value of x is 39°
• $\angle$ P = 88°
• $\angle$Q = 92°
• $\angle$ R = 88°
• $\angle$S = 92°