Question

Given triangle ABC below, if angle B=(x-60)^ and angle C=(x- 45)^ find the measure of angle x

Answer 1

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°