Question

in the triangle below, suppose that $m\angle q=(x + 4)\degree$, $m\angle r=(6x + 8)\degree$, and $m\angle s=(5x)\degree$.
find the degree measure of each angle in the triangle.
$m\angle q = \square\degree$
$m\angle r = \square\degree$
$m\angle s = \square\degree$

Explanation:

Step1: Use triangle angle sum theorem

The sum of angles in a triangle is \(180^\circ\). So, \((x + 4)+(6x + 8)+(5x)=180\).

Step2: Simplify the equation

Combine like terms: \(x+6x + 5x+4 + 8=180\) → \(12x+12 = 180\).

Step3: Solve for \(x\)

Subtract 12 from both sides: \(12x=180 - 12=168\). Divide by 12: \(x=\frac{168}{12}=14\).

Step4: Find \(m\angle Q\)

Substitute \(x = 14\) into \((x + 4)\): \(14+4 = 18\).

Step5: Find \(m\angle R\)

Substitute \(x = 14\) into \((6x + 8)\): \(6\times14+8=84 + 8=92\).

Step6: Find \(m\angle S\)

Substitute \(x = 14\) into \((5x)\): \(5\times14 = 70\).

Answer:

\(m\angle Q=\boxed{18}^\circ\)
\(m\angle R=\boxed{92}^\circ\)
\(m\angle S=\boxed{70}^\circ\)