Question

m∠bca =
m∠abc =

Explanation:

Step1: Apply 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, \(97^{\circ}=(14x - 1)^{\circ}+(2x + 2)^{\circ}\)

Step2: Simplify the equation

Combine like terms: \(97 = 14x-1 + 2x+2\)
\(97=16x + 1\)
Subtract \(1\) from both sides: \(97 - 1=16x\)
\(96 = 16x\)
Divide both sides by \(16\): \(x=\frac{96}{16}=6\)

Step3: Find \(m\angle BCA\)

Substitute \(x = 6\) into \((2x + 2)^{\circ}\)
\(m\angle BCA=(2\times6 + 2)^{\circ}=(12 + 2)^{\circ}=14^{\circ}\)

Step4: Find \(m\angle ABC\)

Substitute \(x = 6\) into \((14x - 1)^{\circ}\)
\(m\angle ABC=(14\times6-1)^{\circ}=(84 - 1)^{\circ}=83^{\circ}\)

Answer:

\(m\angle BCA = 14^{\circ}\), \(m\angle ABC = 83^{\circ}\)