Question

find the value of x.
○ x = 2
○ x = 3
○ x = 33
○ x = 52
(45x)° at q-r, (25x)° at t, (57 + x)° at r-s, triangle t-r-s with q-r-s on a straight line

Explanation:

Step1: Sum of angles in triangle

Sum of angles in $\triangle TRS$ is $180^\circ$: $25x + \angle TRS + \angle TSR = 180^\circ$.

Step2: Linear pair angles

$\angle TRS = 180^\circ - 45x$, $\angle TSR = 180^\circ - (57 + x)$.

Step3: Substitute into triangle sum

$25x + (180 - 45x) + (180 - 57 - x) = 180$.

Step4: Simplify equation

$25x + 180 - 45x + 123 - x = 180$ → $-21x + 303 = 180$ → $-21x = -123$ → $x = 3$.

Answer:

B. x = 3