Question

m∠2=(2x + 28)° and m∠4=(6x + 4)° what is m∠1? 28 140 40 6

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $m\angle2 = m\angle4$. Set up the equation $2x + 28=6x + 4$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $28 = 4x+4$. Then subtract 4 from both sides: $24 = 4x$. Divide both sides by 4, we get $x = 6$.

Step3: Find $m\angle2$

Substitute $x = 6$ into the expression for $m\angle2$: $m\angle2=2x + 28=2\times6+28=12 + 28=40^{\circ}$.

Step4: Use the linear - pair property

$\angle1$ and $\angle2$ form a linear pair, so $m\angle1+m\angle2 = 180^{\circ}$. Then $m\angle1=180 - m\angle2$.

Step5: Calculate $m\angle1$

Since $m\angle2 = 40^{\circ}$, $m\angle1=180 - 40=140^{\circ}$.

Answer:

140