Question

if the measure of ∠a is 105° more than twice the measure of ∠b, and the sum of the measures of the two angles is 180°, what is the measure of each angle? m(∠a)=□° m(∠b)=□°

Explanation:

Step1: Set up equations

Let $m(\angle B)=x$. Then $m(\angle A)=2x + 105$. And we know that $m(\angle A)+m(\angle B)=180$, so $(2x + 105)+x=180$.

Step2: Simplify the equation

Combine like - terms: $2x+x+105 = 180$, which gives $3x+105 = 180$.

Step3: Solve for $x$

Subtract 105 from both sides: $3x=180 - 105$, so $3x=75$. Then divide both sides by 3: $x=\frac{75}{3}=25$.

Step4: Find $m(\angle A)$

Since $m(\angle A)=2x + 105$ and $x = 25$, then $m(\angle A)=2\times25+105=50 + 105=155$.

Answer:

$m(\angle A)=155^{\circ}$
$m(\angle B)=25^{\circ}$