Line AB ∥ CD ∥ Line EF and line QP is their transversal. If Y: z = 3:7 then find the measure of ∠x. (See figure 2.25.)

Given line AB ∥ CD ∥ Line EF and line QP is their transversal.

To find: ∠ X.

AB ∥ CD ∥ EF (linear pair angle) (linear pair angle) means that linear pair is a pair of adjacent, supplementary angle .Adjacent means next to each other ,and supplementary means that measures of the two angles add up to equal 180 °.

X = z (alternate interior angles) …………. (1)

Alternate interior angles are a pair of angles on the inner side of each of those two lines but on opposite side of the transversal.

Y: z = 3:7 (given)

Let the common ratio between y and z be a

X + y = 180° (co -interior angles on the same side of the transversal)

Z + y = 180° (using equation 1)

7a + 3a = 180°

10a = 180°

A = 18°

∴ x = 7a

X = 7× 18°

X = 126°