The value of x in the diagram is 15° and the value of y is 6°
Please find attached the diagram used in answering this question
The figure given is a triangle. A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees
The first step is to determine the value of x.
The value of x can be determined using the exterior angle.
The sum of the two interior opposite angles in a triangle is equal to the external angle
(4x - 7)° + 86° = (9x + 4)°
Combine similar terms
9x - 4x = 86 - 7 - 4
5x = 75
x = 15°
To determine the value of y, first substitute for the value of x in the angle (4x - 7)°
(4x - 7)° = (4x15) - 7 = 53°
The sum of angles in a triangle add up to 180°
53° + 86 + (7y - 1) = 180°
add like terms
138 + 7y = 180
7y = 42
y = 6°
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