Question

1. (6 points) given △abc, m∠a=(3x + 28)°, m∠b=(5x + 52)°, and m∠c=(2x - 10)°. determine the value of x and m∠c.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(3x + 28)+(5x + 52)+(2x-10)=180$.

Step2: Combine like - terms

$(3x+5x + 2x)+(28 + 52-10)=180$, which simplifies to $10x+70 = 180$.

Step3: Solve for x

Subtract 70 from both sides: $10x=180 - 70$, so $10x=110$. Then divide both sides by 10: $x=\frac{110}{10}=11$.

Step4: Find the measure of angle C

Substitute $x = 11$ into the expression for $m\angle C$. $m\angle C=(2x-10)^{\circ}=(2\times11 - 10)^{\circ}=(22-10)^{\circ}=12^{\circ}$.

Answer:

$x = 11$, $m\angle C=12^{\circ}$