Question

a 75° 105°
b 40° 80°
c 5°, 10°
d 25°, 50°
e 35°, 70°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(a + 2a+75^{\circ}=180^{\circ}\).

Step2: Combine like - terms

\(3a+75^{\circ}=180^{\circ}\).

Step3: Isolate the variable

Subtract 75° from both sides: \(3a=180^{\circ}- 75^{\circ}=105^{\circ}\).

Step4: Solve for \(a\)

Divide both sides by 3: \(a = \frac{105^{\circ}}{3}=35^{\circ}\).

Step5: Find \(2a\)

\(2a = 2\times35^{\circ}=70^{\circ}\).

Answer:

E. \(35^{\circ},70^{\circ}\)