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°

Step-by-step 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 = $\frac{1}{2}*(180 - 38)$

m<EDA = $\frac{1}{2}*(142) = 71$

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

$x + 71 = 180$

$x + 71 - 71 = 180 - 71$

$x = 109$

Value of x = 109°