Question

numeric 1 point
find the value of x
m∠a=(9x + 29)°, m∠b=(93 - 5x)°, and m∠c=(10x + 2)°.
answer

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(m\angle A + m\angle B+m\angle C=180^{\circ}\).

Step2: Substitute the given angle - expressions

Substitute \(m\angle A=(9x + 29)^{\circ}\), \(m\angle B=(93 - 5x)^{\circ}\), and \(m\angle C=(10x + 2)^{\circ}\) into the equation: \((9x + 29)+(93 - 5x)+(10x + 2)=180\).

Step3: Combine like - terms

Combine the \(x\) terms and the constant terms: \((9x-5x + 10x)+(29 + 93+2)=180\), which simplifies to \(14x+124 = 180\).

Step4: Isolate the variable \(x\)

Subtract 124 from both sides of the equation: \(14x=180 - 124\), so \(14x=56\).

Step5: Solve for \(x\)

Divide both sides by 14: \(x=\frac{56}{14}=4\).

Answer:

4