Question

find the value of x.
3.
(8x - 30)° (4x + 26)°
12
a
14
14.5
17
find the measure of the missing angle.
4.
75°
? 39°
138°
a
66°
139°
116°

Explanation:

Step1: Apply the exterior angle theorem for problem 3

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(8x - 30=(x - 5)+(4x + 26)\).

Step2: Simplify the right - hand side of the equation

\((x - 5)+(4x + 26)=x - 5+4x + 26=5x+21\). The equation becomes \(8x - 30 = 5x+21\).

Step3: Solve for \(x\)

Subtract \(5x\) from both sides: \(8x-5x - 30=5x - 5x+21\), which gives \(3x-30 = 21\). Then add \(30\) to both sides: \(3x-30 + 30=21 + 30\), so \(3x=51\). Divide both sides by \(3\): \(x=\frac{51}{3}=17\).

Step4: Use the triangle angle sum theorem for problem 4

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the missing angle be \(y\). Then \(y + 75^{\circ}+39^{\circ}=180^{\circ}\).

Step5: Solve for \(y\)

\(y=180^{\circ}-(75^{\circ}+39^{\circ})\). First, calculate \(75^{\circ}+39^{\circ}=114^{\circ}\). Then \(y = 180^{\circ}-114^{\circ}=66^{\circ}\).

Answer:

1. D. \(17\)
2. B. \(66^{\circ}\)