Question

1. solve for the value of x and determine the measure of each angle

x =
$$ m angle a = $$
$$ m angle b = $$
$$ m angle c = $$

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle A + m\angle B+m\angle C = 180^{\circ}\). Substitute the given angle expressions: \(3x+(2x + 1)+(x + 5)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((3x+2x+x)+(1 + 5)=180\), which gives \(6x+6 = 180\).

Step3: Solve for \(x\)

Subtract \(6\) from both sides: \(6x=180 - 6=174\). Then divide both sides by \(6\): \(x=\frac{174}{6}=29\).

Step4: Find \(m\angle A\)

Substitute \(x = 29\) into \(m\angle A=3x\). So, \(m\angle A=3\times29 = 87^{\circ}\).

Step5: Find \(m\angle B\)

Substitute \(x = 29\) into \(m\angle B=2x + 1\). So, \(m\angle B=2\times29+1=58 + 1=59^{\circ}\).

Step6: Find \(m\angle C\)

Substitute \(x = 29\) into \(m\angle C=x + 5\). So, \(m\angle C=29+5=34^{\circ}\).

Answer:

\(x = 29\), \(m\angle A=87^{\circ}\), \(m\angle B=59^{\circ}\), \(m\angle C=34^{\circ}\)