1.

Since ABCD is a rectangle, then

angleABE = 90 degrees

angle ABE + angle BEA + 41 = 180

Substitute the known and solve for angle BEA

angle BEA + 41 = 90

angle BEA = 49 degrees

But,

x + angleBEA + 61 = 180 (angles in a straight line)

x = 180 - 61 - 49

x = 70 degrees

2.

triangle XYZ is equilateral, meaning all angles in it are the same, each 60 degrees.

Therefore,

Angle YZX = 60

But Angle YZX = x + 32 (exterior angles equal to the sum of the two opposite interior angles)

60 = x + 32

Therefore,

x = 28 degrees

3.

Angle QPR = Angle QRP (equal oppo sides, equal opposite angles)

Therefore, 2angleQRP + 64 = 180 (angle sum of a triangle)

Angle QRP = 58 degrees

But angle QRP = x + 35 (exterior angles equal to the sum of the two opposite interior angles)

58 = x + 35

x = 23 degrees

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