Question

problem 15: in △abc, the exterior angle adjacent to ∠c has a measure of 120. if m∠a = 2x and m∠b = x + 15, find the measures of the angles of △abc. after you enter your answer press go. m∠a = m∠b = m∠c =

Explanation:

Step1: Use exterior - angle property

The exterior angle adjacent to $\angle C$ is equal to the sum of $\angle A$ and $\angle B$. So, $2x+(x + 15)=120$.

Step2: Solve the equation for $x$

Combine like - terms: $3x+15 = 120$. Subtract 15 from both sides: $3x=120 - 15=105$. Divide both sides by 3: $x=\frac{105}{3}=35$.

Step3: Find the measure of $\angle A$

Substitute $x = 35$ into the expression for $\angle A$. $m\angle A=2x$, so $m\angle A = 2\times35 = 70$.

Step4: Find the measure of $\angle B$

Substitute $x = 35$ into the expression for $\angle B$. $m\angle B=x + 15$, so $m\angle B=35 + 15 = 50$.

Step5: Find the measure of $\angle C$

The exterior angle adjacent to $\angle C$ is 120. So, $m\angle C=180 - 120=60$. (Or use the fact that the sum of angles in a triangle is 180: $m\angle C=180-(m\angle A + m\angle B)=180-(70 + 55)=55$).

Answer:

$m\angle A = 70$, $m\angle B = 55$, $m\angle C = 55$