Question

angle mon is a straight angle and \\(\overrightarrow{op}\\) bisects \\(\angle moq\\). what is the measure of \\(\angle mop\\)? \\(\bigcirc\\ 29^\circ\\) \\(\bigcirc\\ 58^\circ\\) \\(\bigcirc\\ 61^\circ\\) \\(\bigcirc\\ 122^\circ\\) diagram: straight line m-o-n, oq makes 58° with on, op bisects ∠moq

Explanation:

Step1: Find ∠MOQ

Since ∠MON is a straight angle ($180^\circ$) and ∠NOQ is $58^\circ$, we calculate ∠MOQ as $180^\circ - 58^\circ = 122^\circ$.

Step2: Find ∠MOP

Because $\overrightarrow{OP}$ bisects ∠MOQ, ∠MOP is half of ∠MOQ. So, ∠MOP = $\frac{122^\circ}{2} = 61^\circ$.

Answer:

$61^\circ$ (corresponding to the option "61°")