Given:
m∠B = (x - 60)°
m∠C = (x - 45)°
Opposite angle = x°
Let's find the measure of angle x.
To find the measure of angle x, apply the Exterior Angle Theorem which states that the exterior angle of a triangle is equal to the sum of the two opposite angles.
Thus, we have:
∠B + ∠C = x
(x - 60) + (x - 45) = x
Solve for x.
• Remove the parentheses and combine like terms:
x - 60 + x - 45 = x
x + x - 60 - 45 = x
2x - 105 = x
• Move all terms containing x to the left, then move 105 to the right
2x - x = 105
x = 105°
Therefore, the measure of angle x is 105°
ANSWER:
x = 105°
