Question

if m∠abc=(3m - 15)° and m∠abd=(5m + 59)°, find the value of m such that ∠abc and ∠abd are supplementary.
-37
11
37
5.75

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle ABC + m\angle ABD=180^{\circ}\).
Substitute the given angle - measures: \((3m - 15)+(5m + 59)=180\).

Step2: Combine like - terms

\(3m+5m-15 + 59=180\).
\(8m+44 = 180\).

Step3: Isolate the variable term

Subtract 44 from both sides: \(8m=180 - 44\).
\(8m=136\).

Step4: Solve for m

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

Answer:

17