Question

find the measure of ∠a given the information below.
f = 56°
c = 41°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle with angles \(b\), \(c\), and \(f\), we know \(c = 41^{\circ}\) and \(f=56^{\circ}\). Let's first find angle \(b\).
\[b + c + f=180^{\circ}\]
\[b=180^{\circ}-(c + f)\]
\[b = 180^{\circ}-(41^{\circ}+ 56^{\circ})=180^{\circ}-97^{\circ}=83^{\circ}\]

Step2: Use linear - pair property

Angles \(a\) and \(b\) form a linear - pair. A linear - pair of angles is supplementary, meaning \(a + b=180^{\circ}\).
\[a=180^{\circ}-b\]
Since \(b = 83^{\circ}\), then \(a=180^{\circ}-83^{\circ}=97^{\circ}\)

Answer:

\(97^{\circ}\)