Question

find m∠c.
triangle with vertices a, b, c; angle at a: (21x - 1^circ), angle at b: (26x + 6^circ), angle at c: (11x + 1^circ)
q. find the measure of the indicated angle.

Explanation:

Step1: Sum of angles in a triangle is \(180^\circ\)

The sum of the interior angles of a triangle is \(180^\circ\). So, we can write the equation: \((21x - 1) + (26x + 6) + (11x + 1) = 180\).

Step2: Combine like terms

First, combine the \(x\) terms and the constant terms:
\(21x + 26x + 11x - 1 + 6 + 1 = 180\)
\(58x + 6 = 180\)

Step3: Solve for \(x\)

Subtract 6 from both sides:
\(58x = 180 - 6\)
\(58x = 174\)
Divide both sides by 58:
\(x = \frac{174}{58}\)
\(x = 3\)

Step4: Find \(m\angle C\)

We know that \(m\angle C = 11x + 1\). Substitute \(x = 3\) into this expression:
\(m\angle C = 11(3) + 1\)
\(m\angle C = 33 + 1\)
\(m\angle C = 34^\circ\)

Answer:

\(34^\circ\)