Question

1. solve for $x$ and find the $m\angle r$. the outlined content above was added from outside of formative. $x = square$ degrees $m\angle r=square$ degrees

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, $15x + 2=(40)+(9x + 10)$.

Step2: Simplify the equation

$15x+2 = 40 + 9x+10$. Combine like terms: $15x+2=9x + 50$.

Step3: Isolate the variable $x$

Subtract $9x$ from both sides: $15x-9x+2=9x - 9x+50$, which gives $6x+2 = 50$. Then subtract 2 from both sides: $6x+2 - 2=50 - 2$, so $6x=48$. Divide both sides by 6: $x=\frac{48}{6}=8$.

Step4: Find the measure of $\angle R$

Substitute $x = 8$ into the expression for $m\angle R$. $m\angle R=9x + 10$. So, $m\angle R=9\times8+10=72 + 10=82$.

Answer:

$x = 8$
$m\angle R=82$