Question

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

Explanation:

Identify the given angles

We are given a triangle \(ABC\) with two known interior angles:

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

Apply the triangle angle sum theorem

Using the Triangle Angle Sum theorem, the sum of the 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 measure of angle C

First, add the two known angles:

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

Subtract \(165^\circ\) from both sides to find \(\angle C\):

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

Answer:

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