Arpitha lined up the interior angles of the triangle along the line below.

Question

Triangle A B C. Angle C is 99 degrees. 2 lines extend from a straight line to form 3 angles. From left to right, the angles are A, 22 degrees, C.
What is the measure of angle A?
22°
59°
77°
120°

Answer 1

In a triangle, the sum of the interior angles is always 180 degrees. From the information provided, we know that angle C is 99 degrees and one of the angles in the line is 22 degrees.

Let's denote the measure of angle A as \( A \).

According to the triangle angle sum property, we have:

\[ A + 22^\circ + C = 180^\circ \]

Substituting the known value of angle C (which is 99 degrees):

\[ A + 22^\circ + 99^\circ = 180^\circ \]

Now, combine the known angles:

\[ A + 121^\circ = 180^\circ \]

Next, to find angle A, we subtract 121 degrees from both sides:

\[ A = 180^\circ - 121^\circ \] \[ A = 59^\circ \]

Thus, the measure of angle A is \( 59^\circ \).

So, the answer is \( \boxed{59^\circ} \).