Question

assume lines p and q intersect to form adjacent angles 1 and 2. if m∠1 = (4x − 3)° and m∠2 = (3x + 8)°, find the value of x such that ∠1 is supplementary to ∠2. x = \boxed{}

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\). 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: Combine like terms

Simplify the left side: \(4x+3x - 3 + 8 = 180\) → \(7x + 5 = 180\).

Step4: Solve for x

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

Answer:

\(25\)