In the figure, line l ∥ line m and line p ∥ line q. Find the measures ∠ a, ∠ b, ∠ c and ∠ d.

Open in App

Solution

In the figure, line l ∥ line m and line p ∥ line q. Find the measures ∠ a, ∠ b, ∠ c and ∠ d.

Since, line l || line m (Given)

So, ∠ a = 78 $°$ (Corresponding angles)

Also,

Since, line p || line q (Given)

So, ∠ b = ∠ a (Alternate interior angles)

or, ∠ b = 78 $°$

And,

∠ d = ∠ b (Vertically opposite angles)

or, ∠ d = 78 $°$

Again,

Since, line p || line q (Given)

So, ∠ d + ∠ c = 180 $°$ (Consecutive interior angles)

or, 78 $°$ + ∠ c = 180 $°$

or, ∠ c = 102 $°$

Suggest Corrections

Similar questions

Q. In the adjoining figure. line p ∥ line q. line l ∥ line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

In the given figure, line p || line q and line l and line m are transversals. Measures of some angles are shown.

Hence find the measures of

∠ a, ∠ b, ∠ c, ∠ d .

Q. in figure, line

l i n e p ∥ l i n e q

and line

l

and line

m

are transverses measures of same angles are shown there. Find the measures of

∠ a, ∠ b, ∠ c, ∠ d

Q. In the given figure, line l || line m and line n || p . Find

∠ a, ∠ b, ∠ c .

from the given measure of an angle .

In the given figure, line $p$ is parallel to the line $q$ . Line $l$ and line $m$ are transversals. Measures of some angles are shown. Find the measures of $∠ a$ and $∠ c$ .

Join BYJU'S Learning Program