Question

(d) problem 22: (first taught in lesson 31) find b.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(7x = 4x+60\).
Subtract \(4x\) from both sides: \(7x - 4x=4x + 60-4x\), which gives \(3x = 60\).
Divide both sides by 3: \(x=\frac{60}{3}=20\).

Step2: Use the linear - pair relationship

Since \(7x\) and \(b\) form a linear pair (\(7x + b=180\)), substitute \(x = 20\) into \(7x\).
\(7x=7\times20 = 140\). Then \(b=180 - 7x\).
Substitute \(7x = 140\) into the equation: \(b=180-140\).

Answer:

\(b = 40\)