Question

Please help I've lost all hope on these questions.

Also please show an example of how you solved it. I need the notes

Answer 1

1)

<CPQ+<CPS=180 degrees.

<CPQ=12x+57, <CPS=8x-7

(12x+57)+(8x-7)=180

20x=130

x=6.5

<CPQ=12×6.5+57=135

Answer: <CPQ=135 degrees.

2)

<JSY=<ACK(vertical angles)

<JSY=4x+5, <ACK=2x+15

4x+5=2x+15

2x=10

x=5

<JSY=4×5+5=25

Answer: <JSY=25 degrees.

Answer 2

CPQ = 135

JCY = 25

Explanation:

The two angles form a straight line, so the sum of the angles is 180

8x-7 + 12x+57 = 180

Combine like terms

20x +50 = 180

Subtract 50 from each side

20x+50-50 = 180-50

20x = 130

Divide each side by 20

20x/20 = 130/20

x =6.5

We want to find CPQ

CPQ = 12x+57

=12(6.5) +57

=78+57

135

These angles are vertical angles and vertical angles are equal

4x+5 = 2x+15

Subtract 2x from each side

4x-2x+5 = 2x-2x+15

2x+5 = 15

Subtract 5 from each side

2x+5-5 =15-5

2x = 10

Divide each side by 2

2x/2 = 10/2

x =5

We want to find JCY

JCY = 4x+5

= 4(5)+5

=25