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.

( \bigcirc )-37

( \bigcirc )17

( \bigcirc )37

( \bigcirc )5.75

Explanation:

Step1: Recall supplementary angles property

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

Step2: Combine like terms

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

Step3: Solve for \(m\)

Subtract 44 from both sides: \(8m = 180 - 44\)
\(8m = 136\)
Divide both sides by 8: \(m = \frac{136}{8}\)
\(m = 17\).

Answer:

17