Question

find the measure of ∠a given the measure of ∠b = 170° and the measure of ∠c = 74° in the figure below. ∠a =

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is $360^{\circ}$. So, $\angle a+\angle b+\angle c = 360^{\circ}$.

Step2: Rearrange to solve for $\angle a$

$\angle a=360^{\circ}-\angle b - \angle c$.

Step3: Substitute given values

Substitute $\angle b = 170^{\circ}$ and $\angle c = 74^{\circ}$ into the formula. $\angle a=360^{\circ}-170^{\circ}-74^{\circ}$.

Step4: Calculate

$\angle a = 116^{\circ}$.

Answer:

$116$