Question

what is the measure of angle c? \\( \underline{\quad}^{\circ} \\)

Explanation:

Identify the given angles

We are given a triangle \(ABC\) with:

• \(\angle A = 80^\circ\)
• \(\angle B = 85^\circ\)

State the angle sum theorem

The sum of interior angles in any triangle is always \(180^\circ\).

$$ \angle A + \angle B + \angle C = 180^\circ $$

Substitute the known values

Substitute the given angle measures into the equation:

$$ 80^\circ + 85^\circ + \angle C = 180^\circ $$

Solve for the unknown angle

Simplify and solve for \(\angle C\):

$$ 165^\circ + \angle C = 180^\circ $$

$$ \angle C = 180^\circ - 165^\circ = 15^\circ $$

Answer:

What is the measure of angle C? <blank>15</blank>\(^\circ\)