Question

given that m∠cat = 135°, find the value of x and the m∠cab. m∠cab = (3x + 11)° (2x - 6)°

Explanation:

Step1: Set up equation based on angle - sum

Since \(m\angle CAT=(2x - 9)^{\circ}+(3x + 1)^{\circ}=135^{\circ}\), we first combine like - terms on the left - hand side.
\((2x-9)+(3x + 1)=2x-9+3x + 1=5x-8\). So the equation becomes \(5x-8 = 135\).

Step2: Solve for x

Add 8 to both sides of the equation \(5x-8 = 135\).
\(5x-8 + 8=135 + 8\), which simplifies to \(5x=143\). Then divide both sides by 5.
\(x=\frac{143}{5}=28.6\).

Step3: Find \(m\angle CAB\)

Substitute \(x = 28.6\) into the expression for \(m\angle CAB=3x + 1\).
\(m\angle CAB=3\times28.6+1=85.8 + 1=86.8^{\circ}\).

Answer:

\(x = 28.6\), \(m\angle CAB=86.8^{\circ}\)