A temporary wooden support beam crosses two upright rectangular frames and that are…

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

Problem

A temporary wooden support beam crosses two upright rectangular frames

l

and

m

that are intended to be vertical and parallel. The beam meets frame

l

at point

P

and frame

m

at point

Q

. On the left of the beam the angle between the beam and frame

l

112^\circ

. On the right of the beam, the corresponding angle between the beam and frame

m

(3y - 4)^\circ

. Work out the following: (i) Draw a rough labelled sketch of the situation showing all given angles. (ii) Using the given information, find

y

. (iii) With your value of

y

, calculate the acute angle between the beam and frame

m

on the opposite side from the angle used in part (ii). (iv) Explain, with reasons, whether the two frames can be accepted as parallel.