In the given figure, XOY is a straight line. Find

(i) ∠XOP

(ii) ∠YOP

Since XOY is a straight line, we have:

∠XOP + ∠YOP = 180°

We know from the figure that ∠XOP = (x + 15)° and ∠YOP = (3x + 25)°

Substituting the value of ∠XOP and ∠YOP in above, we get:

⇒ (x + 15)° + (3x + 25)° = 180°

⇒ 4x° + 40° = 180°

⇒ 4x° = 180° - 40°

⇒ 4x° = 140°

⇒ x° = $\dfrac{140^{\circ}}{4}$

⇒ x° = 35°

Now, let's find the measure of each angle by substituting the value of x:

(i) ∠XOP

∠XOP = (x + 15)°

= (35 + 15)°

= 50°

Thus, the measure of ∠XOP is 50°.

(ii) ∠YOP

∠YOP = (3x + 25)°

= (3(35) + 25)°

= (105 + 25)°

= 130°

Thus, the measure of ∠YOP is 130°.