Answer:
- k = 11
- Y = 52°
- Z = 98°
- ∠WXZ = 150°
Explanation:
You want the value of the variable k and the angle measures around triangle XYZ in the given figure.
Exterior angle
The exterior angle at X is equal to the sum of the remote interior angles at Y and Z:
14k -4 = (5x -3) +(11k -23)
14k -4 = 16k -26
7k -2 = 8k -13 . . . . . . divide by 2 (because we can)
11 = k . . . . . . . . . . add 13-7k
The value of k is 11.
Angle Y
Y = (5k -3)° = (5·11 -3)°
Y = 52°
Angle Z
Z = (11k -23)° = (11·11 -23)°
Z = 98°
Angle WXZ
angle WXZ = Y +Z = 52° +98°
angle WXZ = 150°
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Additional comment
The exterior angle at X is the supplement of the adjacent interior angle X. That interior angle is also the supplement of the sum of angles Y and Z. Two angles are equal when their supplements are equal. Hence angle WXZ is the sum of angles Y and Z.
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