Question

your answer is incorrect.

• ( m angle a ): your answer is incorrect.
• ( m angle b ): your answer is incorrect.
• ( m angle c ): one of the digits in your answer is wrong. check your work carefully.

in the triangle below, suppose that ( m angle a=(x + 3)^{circ}, m angle b=(2 x-7)^{circ} ), and ( m angle c=(5 x)^{circ} ).
find the degree measure of each angle in the triangle.

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle A + m\angle B+m\angle C=180^{\circ}\).
Substitute \(m\angle A=(x + 3)^{\circ}\), \(m\angle B=(2x-7)^{\circ}\), and \(m\angle C=(5x)^{\circ}\) into the equation:
\((x + 3)+(2x-7)+5x=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+2x + 5x)+(3 - 7)=180\), which gives \(8x-4 = 180\).

Step3: Solve for \(x\)

Add \(4\) to both sides of the equation: \(8x-4+4=180 + 4\), so \(8x=184\).
Divide both sides by \(8\): \(x=\frac{184}{8}=23\).

Step4: Find \(m\angle A\)

Substitute \(x = 23\) into \(m\angle A=(x + 3)^{\circ}\): \(m\angle A=(23 + 3)^{\circ}=26^{\circ}\).

Step5: Find \(m\angle B\)

Substitute \(x = 23\) into \(m\angle B=(2x-7)^{\circ}\): \(m\angle B=(2\times23-7)^{\circ}=(46 - 7)^{\circ}=39^{\circ}\).

Step6: Find \(m\angle C\)

Substitute \(x = 23\) into \(m\angle C=(5x)^{\circ}\): \(m\angle C=(5\times23)^{\circ}=115^{\circ}\).

Answer:

\(m\angle A = 26^{\circ}\), \(m\angle B = 39^{\circ}\), \(m\angle C = 115^{\circ}\)