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

Question

Triangle A B C. Angle C is 112 degrees and angle B is 30 degrees. 2 lines extend from a horizontal line to form 3 angles. From left to right the angles are 38 degrees, blank, 112 degrees.
What is the measure of angle A?
30°
38°
112°
142°

Answer 1

To find the measure of angle A in triangle ABC, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.

Given:

• Angle C = 112 degrees
• Angle B = 30 degrees

We can find angle A using the following equation:

\[ A + B + C = 180° \]

Substituting the known values:

\[ A + 30° + 112° = 180° \]

Combining the known angles:

\[ A + 142° = 180° \]

Now, subtract 142° from both sides to solve for angle A:

\[ A = 180° - 142° = 38° \]

Thus, the measure of angle A is 38 degrees.