Lines and intersect at point such that they are perpendicular to each other

MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Lines

\ell

and

m

intersect at point

O

such that they are perpendicular to each other. A ray

OP

is drawn inside the right angle formed by

\ell

and

m

. (i) If the angle between

OP

and

\ell

(2y + 15)^{\circ}

and the angle between

OP

and

m

(3y - 5)^{\circ}

, write an equation connecting these two angles. (ii) Solve the equation obtained in part (i) to find the value of

y

. (iii) Hence, find the measure of each of the two angles mentioned in part (i). (iv) Verify that the position of

OP

obtained in part (iii) is possible inside the right angle formed by

\ell

and

m