Question

exterior angle theorem (coloring activity)
find the value of x for each problem.
1.
an image showing a triangle with interior angles \\(62^\circ\\) and \\(80^\circ\\), and an exterior angle \\(x^\circ\\).
2.
an image showing a triangle with interior angles \\(38^\circ\\) and \\(24^\circ\\), and an exterior angle \\(x^\circ\\).
3.
an image showing a triangle with interior angles \\(30^\circ\\) and \\(x^\circ\\), and an exterior angle \\(84^\circ\\).
4.
an image showing a triangle with interior angles \\(x^\circ\\) and \\(70^\circ\\), and an exterior angle \\(114^\circ\\).
5.
an image showing a triangle with interior angles \\(84^\circ\\) and \\(57^\circ\\), and an exterior angle \\(x^\circ\\).
6.
an image showing a triangle with interior angles \\(53^\circ\\) and \\(x^\circ\\), and an exterior angle \\(151^\circ\\).
7.
an image showing a triangle with interior angles \\(62^\circ\\) and \\((7x + 14)^\circ\\), and an exterior angle \\((15x - 4)^\circ\\).
8.
an image showing a triangle with interior angles \\(80^\circ\\) and \\((4x + 4)^\circ\\), and an exterior angle \\((10x + 6)^\circ\\).
9.
an image showing a triangle with interior angles \\(8x^\circ\\) and \\((2x + 8)^\circ\\), and an exterior angle \\((8x - 11)^\circ\\).
10.
an image showing a triangle with interior angles \\((5x + 3)^\circ\\) and \\(8x^\circ\\), and an exterior angle \\((15x - 7)^\circ\\).
11.
an image showing a triangle with interior angles \\(8x^\circ\\) and \\((9x - 5)^\circ\\), and an exterior angle \\((20x - 32)^\circ\\).
12.
an image showing a triangle with interior angles \\(7x^\circ\\) and \\((4x - 5)^\circ\\), and an exterior angle \\((9x + 17)^\circ\\).

Explanation:

Apply the Exterior Angle Theorem

Using the Exterior Angle Theorem knowledge point

$$ \text{Exterior Angle} = \text{Sum of Remote Interior Angles} $$

Solve Questions 1 to 4

Using the Exterior Angle Theorem knowledge point

• Question 1:

$$ x^\circ = 62^\circ + 66^\circ \implies x = 128 $$

• Question 2:

$$ x^\circ = 38^\circ + 24^\circ \implies x = 62 $$

• Question 3:

$$ 84^\circ = 30^\circ + x^\circ \implies x = 84 - 30 = 54 $$

• Question 4:

$$ 114^\circ = 70^\circ + x^\circ \implies x = 114 - 70 = 44 $$

Solve Questions 5 to 8

Using the Exterior Angle Theorem knowledge point

• Question 5:

$$ x^\circ = 84^\circ + 57^\circ \implies x = 141 $$

• Question 6:

$$ 151^\circ = 53^\circ + x^\circ \implies x = 151 - 53 = 98 $$

• Question 7:

$$ 15x - 4 = 62 + (7x + 14) \implies 15x - 4 = 7x + 76 \implies 8x = 80 \implies x = 10 $$

• Question 8:

$$ 10x + 6 = 80 + (4x + 4) \implies 10x + 6 = 4x + 84 \implies 6x = 78 \implies x = 13 $$

Solve Questions 9 to 12

Using the Exterior Angle Theorem knowledge point

• Question 9:

$$ 8x - 11 = (2x + 6) + 5x \implies 8x - 11 = 7x + 6 \implies x = 17 $$

• Question 10:

$$ 15x - 7 = (5x + 3) + 8x \implies 15x - 7 = 13x + 3 \implies 2x = 10 \implies x = 5 $$

• Question 11:

$$ 20x - 32 = 8x + (9x - 5) \implies 20x - 32 = 17x - 5 \implies 3x = 27 \implies x = 9 $$

• Question 12:

$$ 9x + 17 = 7x + (4x - 5) \implies 9x + 17 = 11x - 5 \implies 2x = 22 \implies x = 11 $$

Answer:

No.	Answer
2	\(x = 62\)
3	\(x = 54\)
4	\(x = 44\)
5	\(x = 141\)
6	\(x = 98\)
7	\(x = 10\)
8	\(x = 13\)
9	\(x = 17\)
10	\(x = 5\)
11	\(x = 9\)
12	\(x = 11\)