Question

the diagram shows a triangle. what is the value of a? a =

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(6a+(a + 26)+4a=180\).

Step2: Combine like terms

Combine the terms with \(a\): \((6a+a + 4a)+26=180\), which simplifies to \(11a+26 = 180\).

Step3: Isolate the term with \(a\)

Subtract \(26\) from both sides: \(11a=180 - 26\), so \(11a=154\).

Step4: Solve for \(a\)

Divide both sides by \(11\): \(a=\frac{154}{11}\).

Answer:

\(14\)