Question

1. 62° (7x + 14)° (15x - 4)° 22x+56=160 22x=124 x = 5
2. 80° (10x + 6)° (4x + 4)°
3. (8x - 11)° (2x + 6)° 5x° 15x-5 = 180 15x=185 x = 17
4. 8x° (5x + 3)° (15x - 7)° 28x-41=180 28x=184 x = 5
5. 8x° (9x - 5)° (20x - 32)° 37x-37=160 37x=217 x = 5
6. 7x° (9x + 17)° (4x - 5)° 20x+12=160 20x=168 x = 11

match the question number with the answer below. color the picture accordingly.
blue: 9 red: 5 orange: 35
red: 98 pink: 13 red: 62 blue: 10
black: 141 black: 149 yellow: 17 pink: 54
green: 11

Explanation:

Step1: Recall angle - sum property of a triangle and exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Solve problem 7

For the triangle in problem 7, using the exterior - angle property, we have $(7x + 14)+62=(15x - 4)$.
\[

$$\begin{align*} 7x+14 + 62&=15x-4\\ 7x + 76&=15x-4\\ 76 + 4&=15x-7x\\ 80&=8x\\ x& = 10 \end{align*}$$

\]
There seems to be an error in the hand - written solution.

Step3: Solve problem 8

Using the exterior - angle property: $(4x + 4)+80=(10x + 6)$.
\[

$$\begin{align*} 4x+4+80&=10x + 6\\ 4x+84&=10x+6\\ 84 - 6&=10x-4x\\ 78&=6x\\ x&=13 \end{align*}$$

\]

Step4: Solve problem 9

Using the angle - sum property of a triangle (the sum of interior angles of a triangle is $180^{\circ}$), we have $(8x - 11)+(2x + 6)+5x=180$.
\[

$$\begin{align*} 8x-11+2x + 6+5x&=180\\ (8x+2x + 5x)+(-11 + 6)&=180\\ 15x-5&=180\\ 15x&=185\\ x&=\frac{185}{15}=\frac{37}{3}\approx12.33 \end{align*}$$

\]
There is an error in the hand - written solution.

Step5: Solve problem 10

Using the exterior - angle property: $(5x + 3)+8x=(15x - 7)$.
\[

$$\begin{align*} 5x+3+8x&=15x-7\\ 13x+3&=15x-7\\ 3 + 7&=15x-13x\\ 10&=2x\\ x&=5 \end{align*}$$

\]

Step6: Solve problem 11

Using the exterior - angle property: $(9x - 5)+8x=(20x - 32)$.
\[

$$\begin{align*} 9x-5+8x&=20x-32\\ 17x-5&=20x-32\\ 32 - 5&=20x-17x\\ 27&=3x\\ x&=9 \end{align*}$$

\]
There is an error in the hand - written solution.

Step7: Solve problem 12

Using the exterior - angle property: $(4x - 5)+7x=(9x + 17)$.
\[

$$\begin{align*} 4x-5+7x&=9x + 17\\ 11x-5&=9x+17\\ 11x-9x&=17 + 5\\ 2x&=22\\ x&=11 \end{align*}$$

\]

Answer:

Problem 7: $x = 10$
Problem 8: $x = 13$
Problem 9: $x=\frac{37}{3}\approx12.33$
Problem 10: $x = 5$
Problem 11: $x = 9$
Problem 12: $x = 11$