Question

what is m∠abc?

m∠abc = 75°
m∠abc = 60°
m∠abc = 45°
m∠abc = 15°

Explanation:

Step1: Find the measure of ∠ACB

Since ∠ACB and the \(135^{\circ}\) angle are supplementary (they form a linear - pair), we use the formula \(m\angle ACB=180^{\circ}-135^{\circ}\).
\(m\angle ACB = 45^{\circ}\)

Step2: Use the triangle - angle sum theorem

In \(\triangle ABC\), the sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle ABC=x\). We know that \(m\angle A = 75^{\circ}\) and \(m\angle ACB=45^{\circ}\). Using the formula \(m\angle A+m\angle ABC + m\angle ACB=180^{\circ}\), we substitute the known values: \(75^{\circ}+x + 45^{\circ}=180^{\circ}\).
Combine like terms: \(x+120^{\circ}=180^{\circ}\).
Subtract \(120^{\circ}\) from both sides: \(x=m\angle ABC=180^{\circ}-120^{\circ}\)
\(x = 60^{\circ}\)

Answer:

\(m\angle ABC = 60^{\circ}\)