Question

question
examples
in \\(\triangle pqr\\), \\(m\angle p = (4x + 14)\degree\\), \\(m\angle q = (x + 16)\degree\\), and \\(m\angle r = (3x - 2)\degree\\). what is the value of \\(x\\)?
answer attempt 1 out of 2
\\(x = \\)
submit answer
show examples

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle P + m\angle Q + m\angle R = 180^\circ\).

Step2: Substitute angle expressions

Substitute \(m\angle P=(4x + 14)^\circ\), \(m\angle Q=(x + 16)^\circ\), and \(m\angle R=(3x - 2)^\circ\) into the equation:

$$ (4x + 14)+(x + 16)+(3x - 2)=180 $$

Step3: Combine like terms

Combine the \(x\)-terms and constant terms:

$$ 4x+x+3x + 14+16 - 2=180\\ 8x + 28=180 $$

Step4: Solve for \(x\)

Subtract 28 from both sides:

$$ 8x=180 - 28\\ 8x=152 $$

Divide both sides by 8:

$$ x=\frac{152}{8}=19 $$

Answer:

\(19\)