Question

in \\( \delta vwx, m \angle v = ( x + 8 ) ^ { \circ }, m \angle w = ( 5 x + 9 ) ^ { \circ }, \\) and \\( m \angle x = ( 3 x + 10 ) ^ { \circ }. \\) find \\( m \angle x \\).

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle V+m\angle W + m\angle X=180^{\circ}\).
Substitute the given angle measures: \((x + 8)+(5x + 9)+(3x + 10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+5x + 3x)+(8 + 9+10)=180\).
\(9x+27 = 180\).

Step3: Solve for \(x\)

Subtract 27 from both sides: \(9x=180 - 27\), \(9x=153\).
Divide both sides by 9: \(x=\frac{153}{9}=17\).

Step4: Find \(m\angle X\)

Substitute \(x = 17\) into the expression for \(m\angle X\): \(m\angle X=(3x + 10)^{\circ}\).
\(m\angle X=3\times17+10\).
\(m\angle X=51 + 10=55^{\circ}\).

Answer:

$55^{\circ}$