In the figure, lines m and k are parallel (m ∥ k), cut by a transversal. The angle on line m is labeled s° and the angle on line k is labeled t° (co-interior / same-side interior angles). If s = t + 30, what is the value of t? m k s° t°

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Womens health [Obs] [Gyn] QUESTION #8190

Question 1

In the figure, lines $m$ and $k$ are parallel (m ∥ k), cut by a transversal. The angle on line $m$ is labeled $s°$ and the angle on line $k$ is labeled $t°$ (co-interior / same-side interior angles). If $s = t + 30$, what is the value of $t$?

$30$
$60$
$75$✔️
$80$

Correct Answer Explanation

Since $m \parallel k$, the angles $s°$ and $t°$ are co-interior (same-side interior) angles, which means they are supplementary:

$s + t = 180°$

We are also given: $s = t + 30$

Substituting: $(t + 30) + t = 180$

$2t + 30 = 180$

$2t = 150$

$t = 75°$

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