Question

3
m∠acb=

m∠abc=

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.
Here, \(\angle CAD = 103^{\circ}\), and \(\angle CAD=\angle ACB+\angle ABC\). So, \(103=(3x - 14)+(3x + 9)\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side of the equation: \((3x - 14)+(3x + 9)=3x-14 + 3x+9=6x-5\).
The equation becomes \(6x-5 = 103\).
Add \(5\) to both sides: \(6x=103 + 5=108\).
Divide both sides by \(6\): \(x=\frac{108}{6}=18\).

Step3: Find \(\angle ACB\)

Substitute \(x = 18\) into the expression for \(\angle ACB\): \(\angle ACB=3x-14\).
\(\angle ACB=3\times18-14=54 - 14=40^{\circ}\).

Step4: Find \(\angle ABC\)

Substitute \(x = 18\) into the expression for \(\angle ABC\): \(\angle ABC=3x + 9\).
\(\angle ABC=3\times18+9=54 + 9=63^{\circ}\).

Answer:

\(m\angle ACB = 40^{\circ}\), \(m\angle ABC=63^{\circ}\)