Question

1. find the value of x.

(14x + 4)°
(5x - 1)°
(2x + 9)°

x=

m∠a=

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((14x + 4)+(5x - 1)+(2x + 9)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((14x+5x + 2x)+(4 - 1+9)=180\), which gives \(21x+12 = 180\).

Step3: Solve for \(x\)

Subtract \(12\) from both sides: \(21x=180 - 12\), so \(21x=168\). Then divide both sides by \(21\): \(x=\frac{168}{21}=8\).

Step4: Find \(m\angle A\)

Substitute \(x = 8\) into the expression for \(\angle A\): \(m\angle A=14x + 4\). So \(m\angle A=14\times8+4=112 + 4=116^{\circ}\).

Answer:

\(x = 8\), \(m\angle A=116^{\circ}\)