Question

find the missing angle
∠ c = □□□□ °
solve for each missing angle:
what is the complement of 47°?
□□□□ °
what is the supplement of 153°?
□□□□ °
what is the vertical angle of 12°?
□□□□ °

Explanation:

Step1: Sum of triangle angles is 180°

The sum of interior angles in a triangle is $180^\circ$. For $\triangle ABC$, $\angle A + \angle B + \angle C = 180^\circ$.

Step2: Calculate $\angle C$

Substitute known angles: $\angle C = 180^\circ - 38^\circ - 75^\circ = 67^\circ$

Step3: Find complement of 47°

Complementary angles sum to $90^\circ$. $90^\circ - 47^\circ = 43^\circ$

Step4: Find supplement of 153°

Supplementary angles sum to $180^\circ$. $180^\circ - 153^\circ = 27^\circ$

Step5: Identify vertical angle of 12°

Vertical angles are congruent, so the angle is $12^\circ$.

Answer:

$\angle C = 67^\circ$
Complement of $47^\circ$: $43^\circ$
Supplement of $153^\circ$: $27^\circ$
Vertical angle of $12^\circ$: $12^\circ$