Answer:
m∠a = 30°
m∠b = 30°
m∠c = 105°
Step-by-step explanation:
First, we will find the measure of angle a. This angle is a vertical angle to the 30° angle across from it. Since vertical angles are congruent, we know that m∠a = 30°.
Next, we will find the measurement of angle b. We know that a triangle's interior angles add up to 180 degrees and that their angles can be marked by corresponding arches. Here, we see that both angles a and b are congruent (given by the single arch) and are there is a 90-degree angle. This leads us to believe that m∠a = 30°. 180° = 90° + 30° + 30°, so this answer would make sense.
Lastly, we will find the measure of angle c. A straight line (sometimes referred to as a straight angle) is equal to 180°. m∠c and the 75° share a line, we 180° - 75° = m∠c, so m∠c = 105°.
