Question

given that $ell_1parallelell_2$ and the measure of $angle c = 45^{circ}$, find the measures of angles $a$ and $b$.
$mangle a=$
$mangle b=$
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Explanation:

Step1: Identify corresponding angles

Since $\ell_1\parallel\ell_2$, $\angle a$ and $\angle c$ are corresponding angles. So $m\angle a=m\angle c$.
$m\angle a = 45^{\circ}$

Step2: Identify supplementary angles

$\angle a$ and $\angle b$ are a linear - pair (supplementary angles). So $m\angle a + m\angle b=180^{\circ}$.
$m\angle b=180^{\circ}-m\angle a$
$m\angle b = 180 - 45=135^{\circ}$

Answer:

$m\angle a = 45$
$m\angle b = 135$