Question

question 1 consider the figure below. if ∠1 is twice the size of ∠2, what is the measure of ∠4? 90° 60° 30° 120°

Explanation:

Step1: Use angle - sum property

$\angle1$ and $\angle2$ are supplementary (linear - pair of angles), so $\angle1+\angle2 = 180^{\circ}$. Let $\angle2=x$, then $\angle1 = 2x$. Substituting into the equation $2x + x=180^{\circ}$, we get $3x = 180^{\circ}$.

Step2: Solve for $\angle2$

Dividing both sides of $3x = 180^{\circ}$ by 3, we have $x=\frac{180^{\circ}}{3}=60^{\circ}$, so $\angle2 = 60^{\circ}$.

Step3: Use vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are equal. So $\angle4=\angle2$.

Answer:

B. $60^{\circ}$