Question

10
(13x - 20)° (7x)°
a b d
m∠abc =
1

Explanation:

Step1: Use the linear - pair property

Since \(\angle ABC=(13x - 20)^{\circ}\) and \(\angle CBD=(7x)^{\circ}\) form a linear pair, \(\angle ABC+\angle CBD = 180^{\circ}\).
So, \((13x - 20)+7x=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(13x+7x-20 = 180\), \(20x-20 = 180\).
Add \(20\) to both sides: \(20x=180 + 20\), \(20x=200\).
Divide both sides by \(20\): \(x=\frac{200}{20}=10\).

Step3: Find \(m\angle ABC\)

Substitute \(x = 10\) into the expression for \(\angle ABC\).
\(m\angle ABC=(13x - 20)^{\circ}\), \(m\angle ABC=(13\times10-20)^{\circ}\).
\(m\angle ABC=(130 - 20)^{\circ}\).

Answer:

\(110\)