Question

Find the value of x in each case.

Answer 1

x = 13 deg

Explanation:

As shown in the picture, you have:

CF and CD are perpendicular

=> angle BCF = 90 deg

=> angle BCE + angle ECF = angle BCF = 90 deg

or angle BCE + 64 = 90

=> angle BCE = 90 - 64 = 26 deg

Point A, B, and C are collinear

=> (angle ABE) + angle CBE = 180 deg (1)

Otherwise, as the property of the sum of 3 angles in a triangle:

(angle BEC + angle BCE) + angle CBE = 180 deg (2)

From (1) and (2) you would have:

angle ABE = angle BEC + angle BCE

or

3x = 26 + x

<=> 3x - x = 26

<=> 2x = 26

<=> x = 26/2

<=> x = 13

=> angle BEC = x = 13 deg

=> angle ABE = 3x = 3(13) = 39 deg

Hope this helps!