Question

what are the values of t and u? t = □° u = □°

Explanation:

Step1: Find adjacent - angle to 137°

The adjacent - angle to the $137^{\circ}$ angle on the straight - line $AB$ is $180 - 137=43^{\circ}$. Since this angle and $t$ are vertical angles, $t = 43^{\circ}$.

Step2: Use angle - sum property of a triangle

The triangle has two equal sides (marked with red crosses), so it is isosceles. Let the two base - angles be $t$ and the other base - angle (equal to $t$). The sum of angles in a triangle is $180^{\circ}$. So $u=180 - 2t$. Substituting $t = 43^{\circ}$, we get $u = 180-2\times43=180 - 86 = 94^{\circ}$.

Answer:

$t = 43^{\circ}$, $u = 94^{\circ}$