Question

1. find the m∠opm, if m∠opm=(2y + 11)°, and m∠lpm=(8y - 7)°.

Explanation:

Step1: Assume $\angle OPM$ and $\angle LPM$ are complementary or supplementary. Since no other information is given, assume they are adjacent - angles that form a straight - line (supplementary).

$(2y + 11)+(8y-7)=180$

Step2: Combine like terms.

$2y+8y+11 - 7=180$
$10y + 4=180$

Step3: Isolate the variable term.

$10y=180 - 4$
$10y=176$

Step4: Solve for y.

$y=\frac{176}{10}=17.6$

Step5: Find the measure of $\angle OPM$.

Substitute $y = 17.6$ into the expression for $\angle OPM$.
$m\angle OPM=2y + 11$
$m\angle OPM=2\times17.6+11$
$m\angle OPM=35.2+11$
$m\angle OPM = 46.2^{\circ}$

Answer:

$46.2^{\circ}$