Question

question 4 consider the figure below. let ∠8 = 2x + 7 and ∠7 = 7x - 7. what is the measure of ∠1? 47° 140° 183° 20°

Explanation:

Step1: Use linear - pair property

Since $\angle7$ and $\angle8$ form a linear - pair, $\angle7+\angle8 = 180^{\circ}$. So, $(7x - 7)+(2x + 7)=180$.

Step2: Simplify the equation

Combine like terms: $7x-7 + 2x + 7=180$, which simplifies to $9x=180$. Then solve for $x$: $x=\frac{180}{9}=20$.

Step3: Find the measure of $\angle7$

Substitute $x = 20$ into the expression for $\angle7$: $\angle7=7x - 7=7\times20 - 7=140 - 7 = 133^{\circ}$.

Step4: Use vertical - angle property

$\angle1$ and $\angle7$ are vertical angles. Vertical angles are equal. So, $\angle1=\angle7 = 133^{\circ}$.

Answer:

$133^{\circ}$