Question

try: find angle measures in an intersection of three lines
based on the figure above, what is the value of a?
what is the value of b?
what is the value of c?

Explanation:

Step1: Find the value of $b$

Vertical - angles are equal. Since $b$ and the $60^{\circ}$ angle are vertical - angles, $b = 60^{\circ}$.

Step2: Find the value of $c$

The sum of angles on a straight - line is $180^{\circ}$. The angle adjacent to the $75^{\circ}$ angle and $c$ form a straight - line. So $c=180 - 75=105^{\circ}$.

Step3: Find the value of $a$

The sum of the interior angles of a triangle is $180^{\circ}$. Consider the triangle formed by the three lines. One angle is $b = 60^{\circ}$, another is the angle adjacent to the $75^{\circ}$ angle which is $180 - 75 = 105^{\circ}$, and the third is $a$. So $a=180-(60 + 105)=15^{\circ}$.

Answer:

$a = 15$
$b = 60$
$c = 105$