Question

in the given figure, POR is a straight line and the ray OQ stands on it. Find the value of x. also find Angle poq and angle qor​

Answer 1

${\pink{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➡ The value of x = 34°

➡ The two angles are :

◩ QOR = 142°

◩ QOP = 38°

${\pink{\underline{\underline{\purple{\textsf{\textbf{Explanation : }}}}}}}$

Given that, QOR = 3x + 40°

And, QOP = 2x - 30° lies on a straight line $\rm\overline {PR}$

As we know, The straight line is an obtuse angle which is equal to 180°

❃ According to the question :

⇒ (2x - 30) + (3x + 40) = 180°

⇒ 2x - 30 + 3x + 40 = 180°

⇒ 5x + 10 = 180°

⇒5x = 180 - 10

⇒5x = 170°

⇒x = $\frac{170}{5}$

⇒ x = 34°

Therefore,

The two angles are :

✦ 2x - 30 = 38°

✦ 3x + 40 = 142°

Additional information :

• An obtuse angle is equal to 180° therefore the two angles which are given here lies on a straight line. Hence, we have added to 180° and then got the value of x.