Question

the measures of the angles of a triangle are shown in the figure below. solve for x.
60°
(2x+9)°
(4x+3)°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(60 + (4x + 3) + (2x + 9) = 180\).

Step2: Combine like terms

Simplify the left - hand side: \(60+4x + 3+2x + 9=180\) becomes \(6x+72 = 180\).

Step3: Solve for x

Subtract 72 from both sides: \(6x=180 - 72=108\). Then divide by 6: \(x=\frac{108}{6}=18\).

Answer:

\(x = 18\)