Question

name
geometry 4.1 - 4.2 ticket

1. find the value of x. show work.

a
$m\angle a = 7x$
b
$m\angle c = 4x + 15$

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 \(m\angle A = 7x\), \(m\angle B=33^{\circ}\), and \(m\angle C = 4x + 15\) into the equation:
\(7x+33+(4x + 15)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \((7x+4x)+(33 + 15)=180\), which gives \(11x+48 = 180\)

Step3: Solve for \(x\)

Subtract 48 from both sides: \(11x=180 - 48\), so \(11x=132\)
Divide both sides by 11: \(x=\frac{132}{11}\)

Answer:

\(x = 12\)