Question

solve for x.
(16x + 2)° 114°
12x°
9
in △abc, m∠a = 2x°, m∠b = 6x°, and m∠c = 7x°. what is the value of x?
10
solve for x.
3x°
11
solve for x and y.
54°
y° x° 125°
12

Explanation:

Problem 9

Step1: Use exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(16x + 2+12x=114\).

Step2: Combine like terms

\(28x+2 = 114\).

Step3: Subtract 2 from both sides

\(28x=114 - 2=112\).

Step4: Solve for \(x\)

\(x=\frac{112}{28}=4\).

Step1: Use triangle angle - sum theorem

In \(\triangle ABC\), \(m\angle A+m\angle B+m\angle C = 180^{\circ}\). Substitute \(m\angle A = 2x^{\circ}\), \(m\angle B = 6x^{\circ}\), and \(m\angle C = 7x^{\circ}\) into the equation: \(2x+6x + 7x=180\).

Step2: Combine like terms

\(15x=180\).

Step3: Solve for \(x\)

\(x=\frac{180}{15}=12\).

Step1: Recognize an equilateral triangle (all sides are equal, so all angles are equal)

The sum of angles in a triangle is \(180^{\circ}\). Let each angle be \(3x^{\circ}\). Then \(3x+3x + 3x=180\).

Step2: Combine like terms

\(9x=180\).

Step3: Solve for \(x\)

\(x=\frac{180}{9}=20\).

Answer:

\(x = 4\)

Problem 10