Question

Find the measure of the exterior angle.
(15x+34)
29
(12x+26)

Answer 1

189 degrees

Explanation:

To answer this we need to know the theorem that where the sum of two remote angles equal the exterior angle. therefore we can make the statement 15x + 34 = 29 + 12x + 26

now we do algebra

3x = 31

x= 31/3

we now plug this into the exterior angle

we get 15 * 31/3 + 34

and we get 189 degrees.

Answer 2

41°

Explanation:

Little confused about what exterior angle but for the unlabelled angle in the triangle:

As all angles on a straight line should add up to 180, let the unknown angle be y:

180 = 15x + 34 + y

However, we also know that all angles in a triangle must add up to 180:

y + 29 + 12x + 26

Meaning:

15x + 34 + y = y + 29 + 12x + 26

Step 1 - Subtract y from both sides and add like terms:

15x + 34 + y - y = 12x + 29 + 26 + y - y

15x + 34 = 12x + 55

Step 2 - Subtract 34 from both sides of the equation:

15x + 34 - 34 = 12x + 55 - 34

15x = 12x + 21

Step 3 - Subtract 12x from both sides:

15x - 12x = 12x - 12x + 21

3x = 21

Step 4 - Divide both sides by 3:

3x ÷ 3 = 21 ÷ 3

x = 7

Step 5 - Plug into the first equation:

15x + 34 + y = 180

15(7) + 34 + y = 180

105 + 34 + y = 180

139 + y = 180

y = 180 - 139

y = 41

Hope this helps!