The value of x is 5.
Since triangle ABC is an isoceles triangle, angle A = Angle C(base angles of an isoceles triangle are equal)
Since angle A = 73° and angle C = (8y - 7)°
angle A = angle C
⇒ 73 = 8y - 7
Adding 7 to both sides, we have
73 + 7 = 8y - 7 + 7
80 = 8y
Dividing both sides by 8, we have
y = 80/8
y = 10
Also, angle A + angle B + angle C = 180° (sum of angles in a triangle)
73 + 6x + 4 + 8y - 7 = 180
Collecting like terms, we have
73 + 4 - 7 + 6x + 8y = 180
6x + 8y + 70 = 180
Subtracting 70 from both sides, we have
6x + 8y + 70 - 70 = 180 - 70
6x + 8y = 110
Making x subject of the formula, we have
6x = 110 - 8y
x = (110 - 8y)/6
Substituting the value of y into the equation, we have
x = (110 - 8y)/6
x = (110 - 8 × 10)/6
x = (110 - 80)/6
x = 30/6
x = 5
So, the value of x is 5.
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