Question

question 6/25
6 directions - use the triangle angle sum theorem to find k. then find the angle measure of 3k:
write an equation using the triangle sum theorem:
solve for k =
find the measure of unknown angle = degrees.

Explanation:

Step1: Apply triangle - sum theorem

The sum of interior angles of a triangle is 180°. So the equation is \(48 + 84+3k=180\).

Step2: Simplify the left - hand side

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

Step3: Isolate the variable term

Subtract 132 from both sides: \(3k=180 - 132\), which gives \(3k = 48\).

Step4: Solve for k

Divide both sides by 3: \(k=\frac{48}{3}=16\).

Step5: Find the measure of 3k

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

Answer:

Write an equation using the Triangle Sum Theorem: \(48 + 84+3k=180\)
Solve for \(k = 16\)
Find the measure of unknown angle = 48 degrees