Question

andrew constructed a triangle so that $\angle 1$ and $\angle 2$ were the same size and $\angle 3$ measured $80^{\circ}$.
what is the measure of $\angle 1$?
$\bigcirc$ $50^{\circ}$
$\bigcirc$ $60^{\circ}$
$\bigcirc$ $100^{\circ}$
$\bigcirc$ $80^{\circ}$

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$.

Step2: Set up equation for angles

Let $m\angle1 = m\angle2 = x$. Then $x + x + 80^\circ = 180^\circ$.

Step3: Simplify and solve for x

Combine like terms: $2x + 80^\circ = 180^\circ$.
Subtract $80^\circ$: $2x = 180^\circ - 80^\circ = 100^\circ$.
Divide by 2: $x = \frac{100^\circ}{2} = 50^\circ$.

Answer:

$50^\circ$