Question

1. if $mangle1=(4x - 3)^{circ}$ and $mangle2=(3x + 8)^{circ}$, find the value of $x$ such that $angle1$ is supplementary to $angle2$.

Explanation:

Step1: Recall supplementary - angle property

If two angles are supplementary, their sum is 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).

Step2: Substitute angle - measures

Substitute \(m\angle1=(4x - 3)^{\circ}\) and \(m\angle2=(3x + 8)^{\circ}\) into the equation: \((4x-3)+(3x + 8)=180\).

Step3: Simplify the left - hand side

Combine like terms: \(4x+3x-3 + 8=180\), which simplifies to \(7x+5 = 180\).

Step4: Solve for x

Subtract 5 from both sides: \(7x=180 - 5=175\). Then divide both sides by 7: \(x=\frac{175}{7}=25\).

Answer:

\(x = 25\)