Question

1. find m∠s. x=12 132=11x 140° j r 3x+4 8x+4 t s

Explanation:

Step1: Recall exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, $\angle JR S = 140^{\circ}$ is an exterior angle, and the two non - adjacent interior angles are $\angle S$ (with measure $3x + 4$) and $\angle T$ (with measure $8x+4$). So, $140=(3x + 4)+(8x + 4)$.

Step2: Simplify the equation

Combine like terms: $140=3x+8x + 4 + 4=11x+8$.
Subtract 8 from both sides: $140 - 8=11x$, so $132 = 11x$.
Divide both sides by 11: $x=\frac{132}{11}=12$.

Step3: Find $m\angle S$

Substitute $x = 12$ into the expression for $m\angle S$, which is $3x + 4$.
$m\angle S=3\times12 + 4=36 + 4 = 40$.

Answer:

$m\angle S = 40^{\circ}$