Question

From the given figure 7 ,find the value of x if AB is parallel CF and AE = DE, angle BAE = 38°.

Answer 1

*see the given given in the attachment below

Answer:

x = 109°

Explanation:

Since AB is parallel to CF, m<BAE = m<AED = 38° (alternate interior angles are congruent)

Since AE = DE, ∆AED is an isosceles ∆.

The two base angles of any given isosceles ∆ are said to be congruent.

This means, m<EAD = m<EDA = ½(180 - m<AED)

m<EDA =
`(1)/(2)*(180 - 38)`

m<EDA =
`(1)/(2)*(142) = 71`

x + m<EDA = 180° (angle on a straight line)

`x + 71 = 180`

`x + 71 - 71 = 180 - 71`

`x = 109`

Value of x = 109°