In the accompanying diagram, ABCD is a
rectangle, E is a point on CD, M<DAE = 30, and
m<CBE = 20. What is m<x?
A. 25
C. 60
B. 50
D. 70

Given:

m∠DAE = 30°

m∠CBE = 20°

To find:

The value of x.

Solution:

In rectangle, all angles are right angle.

m∠A = m∠B = m∠C = m∠D = 90°

m∠EDA + m∠EAB = 90°

30° + m∠EAB = 90°

m∠EAB = 90° - 30°

m∠EAB = 60°

Similarly, m∠CBE + m∠EBA = 90°

20° + m∠EBA = 90°

m∠EBA = 90° - 20°

m∠EBA = 70°

In triangle AEB,

Sum of all angles in a triangle = 180°

m∠EAB + m∠AEB +m∠EBA = 180°

60° + x° + 70° = 180°

130° + x° = 180°

Subtract 130° from both sides, we get

x° = 50°

x = 50

The value of x is 50.

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