Question

exterior angle theorem (coloring activity)
find the value of x for each problem.

1.
image showing a triangle with interior angles 50^circ, 80^circ and an exterior angle x^circ

2.
image showing a triangle with interior angles 30^circ, 24^circ and an exterior angle x^circ

3.
image showing a triangle with interior angles 30^circ, x^circ and an exterior angle 84^circ

4.
image showing a triangle with interior angles x^circ, 70^circ and an exterior angle 118^circ

5.
image showing a triangle with interior angles x^circ, 57^circ and an exterior angle 84^circ

6.
image showing a triangle with interior angles 53^circ, x^circ and an exterior angle 101^circ

7.
image showing a triangle with interior angles 52^circ, (7x + 14)^circ and an exterior angle (15x - 10)^circ

8.
image showing a triangle with interior angles (10x + 8)^circ, 60^circ and an exterior angle (14x + 4)^circ

9.
image showing a triangle with interior angles (8x - 11)^circ, 5x^circ and an exterior angle (12x + 5)^circ

10.
image showing a triangle with interior angles (5x + 3)^circ, 6x^circ and an exterior angle (10x + 7)^circ

11.
image showing a triangle with interior angles 6x^circ, (20x - 52)^circ and an exterior angle (24x - 32)^circ

12.
image showing a triangle with interior angles 7x^circ, (4x + 5)^circ and an exterior angle (9x + 17)^circ

match the question number with the answer below. color the picture accordingly.

Explanation:

Set up equations using the Exterior Angle Theorem

Using the Exterior Angle Theorem knowledge point
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

• Question 1: \(x = 50^\circ + 80^\circ\)
• Question 2: \(x + 30^\circ = 115^\circ\)
• Question 3: \(30^\circ + x = 84^\circ\)
• Question 4: \(x + 70^\circ = 118^\circ\)
• Question 5: \(x + 57^\circ = 84^\circ\)
• Question 6: \(x + 53^\circ = 151^\circ\)
• Question 7: \((7x + 14)^\circ + 52^\circ = (15x - 6)^\circ\)
• Question 8: \((10x + 8)^\circ + 60^\circ = (18x + 4)^\circ\)
• Question 9: \((8x - 11)^\circ + 5x^\circ = (12x + 5)^\circ\)
• Question 10: \((5x + 5)^\circ + 6x^\circ = (12x - 7)^\circ\)
• Question 11: \(8x^\circ + (9x - 3)^\circ = (20x - 21)^\circ\)
• Question 12: \((8x + 12)^\circ + 7x^\circ = (18x - 6)^\circ\)

Solve equations for Questions 1 to 6

Using the Exterior Angle Theorem knowledge point

• Question 1:

$$x = 130$$

• Question 2:

$$x = 115 - 30 = 85$$

• Question 3:

$$x = 84 - 30 = 54$$

• Question 4:

$$x = 118 - 70 = 48$$

• Question 5:

$$x = 84 - 57 = 27$$

• Question 6:

$$x = 151 - 53 = 98$$

Solve equations for Questions 7 to 9

Using the Exterior Angle Theorem knowledge point

• Question 7:

$$
LATEXBLOCK0
$$

• Question 8:

$$
LATEXBLOCK1
$$

• Question 9:

$$
LATEXBLOCK2
$$

Solve equations for Questions 10 to 12

Using the Exterior Angle Theorem knowledge point

• Question 10:

$$
LATEXBLOCK3
$$

• Question 11:

$$
LATEXBLOCK4
$$

• Question 12:

$$
LATEXBLOCK5
$$

Answer:

No.	Answer
2	\(x = 85\)
3	\(x = 54\)
4	\(x = 48\)
5	\(x = 27\)
6	\(x = 98\)
7	\(x = 9\)
8	\(x = 8\)
9	\(x = 16\)
10	\(x = 12\)
11	\(x = 6\)
12	\(x = 6\)