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 $(7x + 14)+62=(15x - 4)$.

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

Step3: Solve problem 8

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

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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 $(8x - 11)+(2x + 6)+5x=180$.

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There is an error in the hand - written solution.

Step5: Solve problem 10

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

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Step6: Solve problem 11

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

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There is an error in the hand - written solution.

Step7: Solve problem 12

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

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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: $x = 11$