Question

Please help and maybe explain if it’s not clear enough:

Answer 1

Answer:

Step-by-step explanation:

Remark.

• The angle marked 50 degrees is an exterior angle.
• The two angles you seek, are called remote interior angles, because they are (neither of them) the supplement to the 50 degree angle.
• The theorem you use is that the two remote interior angles add to the exterior angle.

Equation

6x + 2 + 9x - 12 = 50                      Combine like terms

Solution

6x + 9x + 2 - 12 = 50                       Combine

15x - 10 = 50                                    Add 10

15x - 10 + 10 = 50 + 10                     Combine

15x = 60                                           Divde by 15

15x/15 = 60/15

x = 4

<CAB = 6x + 2

<CAB = 6*4 + 2

<CAB = 26

<CBA = 9x - 12

<CBA = 9*4 - 12

<CBA = 24

Answer

<CAB = 26

<CBA = 24

Answer 2

Answers:

• x = 4
• angle CAB = 26 degrees
• angle ABC = 24 degrees

Depending on your teacher, you may or may not have to input the word "degrees" or the degree symbol.

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Explanation:

We use the remote interior angle theorem.

This says to add two interior angles, and the sum is equal to the exterior angle that is not adjacent to any of the interior ones. Hence the "remote".

(angle CAB) + (angle ABC) = exterior angle

(6x+2) + (9x-12) = 50

15x-10 = 50

15x = 50+10

15x = 60

x = 60/15

x = 4 is the first answer

We can then find the interior angles

angle CAB = 6x+2 = 6(4)+2 = 24+2 = 26 degrees is the second answer

angle ABC = 9x-12 = 9(4)-12 = 36-12 = 24 degrees is the third answer

Then notice how 26+24 = 50 to help confirm the answers.