Question

problem 21: (lesson 30) if 2a = b, find c in terms of a.

Explanation:

Step1: Use the triangle - angle - sum theorem

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

Step2: Substitute \(b = 2a\) into the equation

Substitute \(b\) with \(2a\) in the equation \(a + b + c=180\). We get \(a+2a + c=180\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \(3a + c=180\).

Step4: Solve for \(c\)

Subtract \(3a\) from both sides of the equation. \(c=180 - 3a\).

Answer:

\(c = 180-3a\)