Question

9
7x + 19
60°
11x - 89
7
(8x - 55)°
(5x - 7)°
8
(4x + 8)°
10
(11x - 65)°
29°
© gina wilson (all things algebra®, llc), 2014 - 2020
x = 7
x = 4

Explanation:

Step1: Analyze the triangle in problem 9

Since two angles are \(60^{\circ}\), it is an equilateral triangle. So \(7x + 19=11x - 89\).

$$\begin{align*} 11x-7x&=19 + 89\\ 4x&=108\\ x&=27 \end{align*}$$

Step2: Analyze the triangle in problem 7

It is an isosceles triangle. So \(8x-55 = 5x-7\).

$$\begin{align*} 8x-5x&=-7 + 55\\ 3x&=48\\ x&=16 \end{align*}$$

Step3: Analyze the triangle in problem 8

It is an equilateral triangle. So \(4x + 8=60\).

$$\begin{align*} 4x&=60 - 8\\ 4x&=52\\ x&=13 \end{align*}$$

Step4: Analyze the triangle in problem 10

It is an isosceles triangle. So \(11x-65+29 = 90\).

$$\begin{align*} 11x-36&=90\\ 11x&=90 + 36\\ 11x&=126\\ x&=12 \end{align*}$$

Answer:

1. \(x = 16\)
2. \(x = 13\)
3. \(x = 27\)
4. \(x = 12\)