Question

directions - use the triangle angle sum theorem to find k. then find the angle measure of 3k
4
84°
48° 3k°
triangle angle sum theorem = 180
k = 16
measure of unknown angle = i degrees.

Explanation:

Step1: Apply triangle angle sum theorem

According to the triangle angle sum theorem, the sum of interior angles of a triangle is \(180^{\circ}\). So, \(48 + 84+3k=180\).

Step2: Simplify the left - hand side

\(48 + 84+3k=(48 + 84)+3k=132 + 3k\). Then the equation becomes \(132+3k = 180\).

Step3: Solve for \(k\)

Subtract \(132\) from both sides: \(3k=180 - 132\). So, \(3k = 48\). Divide both sides by \(3\): \(k=\frac{48}{3}=16\).

Step4: Find the measure of \(3k\)

Substitute \(k = 16\) into \(3k\). Then \(3k=3\times16 = 48\).

Answer:

\(48\)