Question

find each angle measure in the figure. (x + 30)° x° 2x° 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

Combine the $x$ terms on the left - hand side: $(x+x + 2x)+30=180$, which simplifies to $4x+30 = 180$.

Step3: Solve for $x$

Subtract 30 from both sides: $4x=180 - 30=150$. Then divide both sides by 4: $x=\frac{150}{4}=37.5$.

Step4: Find each angle measure

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:

The angle measures are $37.5^{\circ}$, $67.5^{\circ}$ and $75^{\circ}$.
$x+(x + 30)+2x=180$
$x = 37.5$