Let and be two parallel lines

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

Problem

Let

AB

and

CD

be two parallel lines. A transversal

EF

meets

AB

G

and

CD

H

. The measure of

\angle AGH

\left(\dfrac{5x}{3} + 12\right)^{\circ}

, while its co–interior partner

\angle GHD

measures

\left(\dfrac{2x}{3} + 6\right)^{\circ}

. A different transversal

JK

meets

AB

P

such that the exterior angle at

P

corresponding to

\angle AGH

(4y - 3)^{\circ}

. Use the information to complete the tasks below. (i) Form the equation in

x

arising from the co–interior angles on transversal

EF

.},{ (ii) Form the equation in

y

using the corresponding angles on transversal

JK

.},{ (iii) Find the values of

x

and

y

.},{ (iv) Compute the numerical measures of

\angle AGH

\angle GHD

and the exterior angle at

P