Question

the diagram shows a triangle.
what is the value of a?
write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(50+(2a - 18)+4a=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(50-18+2a + 4a=180\), which gives \(32 + 6a=180\).

Step3: Solve for \(a\)

Subtract 32 from both sides: \(6a=180 - 32\), so \(6a=148\). Then divide both sides by 6: \(a=\frac{148}{6}\approx24.7\).

Answer:

\(24.7\)