Question

if (mangle abc=(3m - 15)^{circ}) and (mangle abd=(5m + 59)^{circ}), find the value of (m) such that (angle abc) and (angle abd) are supplementary.
-37
17
37
5.75

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle ABC + m\angle ABD=180^{\circ}\).

Step2: Substitute the given angle - expressions

Substitute \(m\angle ABC=(3m - 15)^{\circ}\) and \(m\angle ABD=(5m + 59)^{\circ}\) into the equation: \((3m-15)+(5m + 59)=180\).

Step3: Combine like - terms

Combine the \(m\) terms and the constant terms: \(3m+5m-15 + 59=180\), which simplifies to \(8m+44 = 180\).

Step4: Isolate the variable term

Subtract 44 from both sides of the equation: \(8m=180 - 44\), so \(8m=136\).

Step5: Solve for \(m\)

Divide both sides by 8: \(m=\frac{136}{8}=17\).

Answer:

17