Question

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Answer 1

1. KLP + PLM = 180 degrees (straight line)

2. 3x + angle PLM = 180 degrees

3. angle PLM = 180 - 3x

4. PMN = P + PLM (Exterior angle)

5. 2x + 72 = x + 180 - 3x

6. x = 27

Explanation:

ngl i didnt really get this i i kinda have a some what idea on what this is

The exterior angles of the triangle added to their corresponding interior angles equal 180 degrees by virtue of the sum of angles on a straight line.

As such the interior angles are

1. 180 - (x+ 3)

2. 180 - (2x+ 1)

3. 180 - (3x - 4)

Given that the sum of angles in a triangle is 180 degrees

180 - (x+ 3) + 180 - (2x+ 1) + 180 - (3x - 4) = 180

540 - 6x = 180

6x = 540 - 180

6x = 360

x = 60

The exterior angles are

x + 3 = 60 + 3 = 63

2x + 1 = 2(60) + 1 = 121

and

3x - 4 = 3(60) - 4 = 180 - 4 = 176

Answer 2

1. KLP + PLM = 180 degrees (straight line)

2. 3x + angle PLM = 180 degrees

3. angle PLM = 180 - 3x

4. PMN = P + PLM (Exterior angle)

5. 2x + 72 = x + 180 - 3x

6. x = 27

Explanation:

1. Notice that angle KLP + angle PLM is a straight line, so KLP + PLM = 180 degrees (straight line)

2. angle KLP = 3x, so

3x + angle PLM = 180 degrees

3. angle PLM = 180 - 3x

4. PMN = P + PLM (Exterior angle)

5. 2x + 72 = x + 180 - 3x

6. 5 gives 4x = 108, so x = 27