In the given figure, XOY is a straight line. Find (i) ∠XOP (ii) ∠YOP

Question

KnowledgeBoat · Accepted Answer

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° = ⇒ 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°.

Mathematics

In the given figure, XOY is a straight line. Find
(i) ∠XOP
(ii) ∠YOP

Lines & Angles

Related Questions

Find an angle which is 5° more than four times its supplement.

In the given figure, AOB is a straight line. Find the measure of ∠AOC.

In the given figure, PQR is a straight line. Find the value of x.

In the given figure BC is produced on both sides to points D and E respectively. Find the values of x and y.