Question

find each angle measure in the figure. the angle measures are □°, □° and □°. use the equation to justify your answer. x+(x + 30)+2x=□ x = □

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $x+(x + 30)+2x=180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side, we get $(1 + 1+2)x+30=180$, which simplifies to $4x+30 = 180$.

Step3: Isolate the variable term

Subtract 30 from both sides of the equation: $4x+30−30=180 - 30$, resulting in $4x=150$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{150}{4}=37.5$.

Step5: Find the angle measures

The first angle is $x = 37.5^{\circ}$.
The second angle is $x + 30=37.5+30 = 67.5^{\circ}$.
The third angle is $2x=2\times37.5 = 75^{\circ}$.

Answer:

37.5, 67.5, 75; 180; 37.5