Answer:
The measure of angle x is 50 degrees
Step-by-step explanation:
we know that
----> equation A
----> equation B
solve the system by substitution
substitute equation B in equation A
solve for y
Find the measure of angle x
therefore
The measure of angle x is 50 degrees
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
Answer:
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Step-by-step explanation:
