Question

in $\triangle opq$, $pq = 18$, $qo = 10$, and $op = 15$. which list has the angles of $\triangle opq$ in order from largest to smallest?
answer
\\( \circ \\) $m\angle p$, $m\angle q$, $m\angle o$ \\( \circ \\) $m\angle q$, $m\angle o$, $m\angle p$
\\( \circ \\) $m\angle q$, $m\angle p$, $m\angle o$ \\( \circ \\) $m\angle o$, $m\angle p$, $m\angle q$
\\( \circ \\) $m\angle p$, $m\angle o$, $m\angle q$ \\( \circ \\) $m\angle o$, $m\angle q$, $m\angle p$

Explanation:

Step1: Match sides to opposite angles

In $\Delta OPQ$:

• Side $PQ=18$ is opposite $\angle O$
• Side $OP=15$ is opposite $\angle Q$
• Side $QO=10$ is opposite $\angle P$

Step2: Order sides from largest to smallest

$18 > 15 > 10$, so $PQ > OP > QO$

Step3: Apply triangle angle-side relationship

Largest side faces largest angle, so $\angle O > \angle Q > \angle P$

Answer:

$\boldsymbol{m\angle O, m\angle Q, m\angle P}$