Question

1. find m∠qbc if m∠abc = 177° and m∠abq = 40°.

Explanation:

Step1: Identify angle - relationship

We know that $\angle ABC=\angle ABQ+\angle QBC$.

Step2: Solve for $\angle QBC$

Let $m\angle QBC = x$. Given $m\angle ABC = 177^{\circ}$ and $m\angle ABQ = 40^{\circ}$, we have the equation $x + 40=177$. Subtracting 40 from both sides of the equation: $x=177 - 40$.
$x = 137^{\circ}$

Answer:

$m\angle QBC=137^{\circ}$