# 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. In triangle \(ABC\), \(\angle DAC\) is an exterior angle. So, \(97^{\circ}=(14x - 1)^{\circ}+(2x + 2)^{\circ}\). \[ \begin{align*} 97&=14x-1 + 2x+2\\ 97&=16x+1\\ 16x&=97 - 1\\ 16x&=96\\ x&=6 \end{align*} \] ## Step2: Find \(m\angle BCA\) Substitute \(x = 6\) into the expression for \(\angle BCA=(2x + 2)^{\circ}\). \[ \begin{align*} \angle BCA&=(2\times6+2)^{\circ}\\ &=(12 + 2)^{\circ}\\ &=14^{\circ} \end{align*} \] ## Step3: Find \(m\angle ABC\) Substitute \(x = 6\) into the expression for \(\angle ABC=(14x - 1)^{\circ}\). \[ \begin{align*} \angle ABC&=(14\times6-1)^{\circ}\\ &=(84-1)^{\circ}\\ &=83^{\circ} \end{align*} \] # Answer: \(m\angle BCA = 14^{\circ}\), \(m\angle ABC=83^{\circ}\)

m∠bca = m∠abc =

QUESTION IMAGE

Question

m∠bca =
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. In triangle \(ABC\), \(\angle DAC\) is an exterior angle. So, \(97^{\circ}=(14x - 1)^{\circ}+(2x + 2)^{\circ}\).

$$ LATEXBLOCK0 $$

Step2: Find \(m\angle BCA\)

Substitute \(x = 6\) into the expression for \(\angle BCA=(2x + 2)^{\circ}\).

$$ LATEXBLOCK1 $$

Step3: Find \(m\angle ABC\)

Substitute \(x = 6\) into the expression for \(\angle ABC=(14x - 1)^{\circ}\).

$$ LATEXBLOCK2 $$

Answer:

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