Question

find the measures of each labeled angle. give a reason for your solution.

Explanation:

Step1: Find angle a

The 145 - degree angle and angle a are supplementary (linear - pair of angles). The sum of supplementary angles is 180 degrees. So, $a = 180 - 145$.
$a=35^{\circ}$

Step2: Find angle b

Angle b and the 40 - degree angle are vertical angles. Vertical angles are equal. So, $b = 40^{\circ}$.

Step3: Find angle c

Angle c and angle b are supplementary (linear - pair of angles). So, $c=180 - b$. Substituting $b = 40^{\circ}$, we get $c = 180 - 40=140^{\circ}$.

Step4: Find angle d

Angle d and the 40 - degree angle are supplementary (linear - pair of angles). So, $d = 180 - 40=140^{\circ}$.

Answer:

a: 35, b: 40, c: 140, d: 140