Question

1. if the sum of the angles of a triangle equals 180 degrees, write and use an equation to solve for x, then find the m∠a

equation:
x =
m∠a =

Explanation:

Step1: Set up the equation

Since the sum of angles in a triangle is 180 degrees and one angle is 90 degrees and the other two non - right angles are \(7x + 3\) each, the equation is \(90+(7x + 3)+(7x + 3)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(90 + 14x+6 = 180\), which simplifies to \(14x+96 = 180\).

Step3: Isolate the variable term

Subtract 96 from both sides: \(14x=180 - 96\), so \(14x = 84\).

Step4: Solve for x

Divide both sides by 14: \(x=\frac{84}{14}=6\).

Step5: Find \(m\angle A\)

Substitute \(x = 6\) into the expression for \(\angle A\) which is \(7x + 3\). So \(m\angle A=7\times6 + 3=42 + 3=45\).

Answer:

Equation: \(90+(7x + 3)+(7x + 3)=180\)
\(x = 6\)
\(m\angle A=45\)