Question

in the triangle below, find the measurements of the unknown angles. a. 75°, 105° b. 40°, 80° c. 5°, 10° d. 25°, 50° e. 35°, 70°

Explanation:

Step1: Recall angle - sum property

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

Step2: Combine like - terms

Combining the $x$ terms, we get $3x + 75^{\circ}=180^{\circ}$.

Step3: Isolate the variable

Subtract $75^{\circ}$ from both sides: $3x=180^{\circ}- 75^{\circ}=105^{\circ}$.

Step4: Solve for $x$

Divide both sides by 3: $x=\frac{105^{\circ}}{3}=35^{\circ}$.

Step5: Find the other angle

The other angle is $2x$, so $2x = 2\times35^{\circ}=70^{\circ}$.

Answer:

E. $35^{\circ},70^{\circ}$