two parallel lines, e and f, are crossed by two transversals. what is the measure of ∠15? m∠15 = 77° m∠15 =…

Explanation:

Step1: Identify corresponding angles

Since lines $e$ and $f$ are parallel and are crossed by transversal $d$, $\angle12$ and $\angle16$ are corresponding - angles, so $m\angle16 = m\angle12$. Given $m\angle12 = 97^{\circ}$, then $m\angle16=97^{\circ}$.

Step2: Use linear - pair property

$\angle15$ and $\angle16$ form a linear pair. The sum of the measures of angles in a linear pair is $180^{\circ}$. So $m\angle15 + m\angle16=180^{\circ}$.

Step3: Solve for $m\angle15$

Substitute $m\angle16 = 97^{\circ}$ into the equation $m\angle15 + m\angle16=180^{\circ}$. We get $m\angle15=180^{\circ}-m\angle16$. Then $m\angle15 = 180 - 97=83^{\circ}$.

Answer:

$m\angle15 = 83^{\circ}$