Question

unit 4 test
find m∠c.
(9x - 26)°
(2x - 12)°
(4x + 43)°

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $9x - 26=(2x - 12)+(4x + 43)$.

Step2: Simplify the right - hand side

$(2x - 12)+(4x + 43)=2x-12 + 4x+43=6x + 31$. So the equation becomes $9x - 26=6x + 31$.

Step3: Solve for x

Subtract $6x$ from both sides: $9x-6x - 26=6x-6x + 31$, which simplifies to $3x-26 = 31$. Then add 26 to both sides: $3x-26 + 26=31 + 26$, so $3x=57$. Divide both sides by 3: $x = 19$.

Step4: Find $m\angle C$

Substitute $x = 19$ into the expression for $m\angle C$ which is $4x + 43$. So $m\angle C=4\times19+43$.
$m\angle C=76 + 43=119^{\circ}$.

Answer:

$119^{\circ}$