Question

the measures of the angles of a triangle are shown in the figure below. solve for x. 43° 109° (2x - 10)°

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(43+(2x - 10)+109=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \((43-10 + 109)+2x=180\).
\(142+2x=180\).

Step3: Solve for \(x\)

Subtract \(142\) from both sides: \(2x=180 - 142\).
\(2x = 38\).
Divide both sides by \(2\): \(x=\frac{38}{2}=19\).

Answer:

\(x = 29\)