Question

I genuinely have no clue how to do them15 here and 15 on another post

Camelle asked Nov 5, 2023

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Kunchok Tashi · Answer 1 · 2023-11-10T11:22:04+0000

Given,

Angle 2 = 40

Angle 4 = 60

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Angle 5 is vertical angle to Angle 2. So, it is same as angle 2.

Angle 5 = 40

Angle 1 is vertical angle to Angle 4. So, Angle 1 = Angle 4.

Angle 1 = 60

Angles 1 through 6 are a ciricular angle, that is 360 degrees.

Let angle 3 and angle 6 be equal and "x" [vertical angles]. Thus,

$\begin{gathered} \angle1+\angle2+\angle3+\angle4+\angle5+\angle6=360 \\ 60+40+x+60+40+x=360 \\ 200+2x=360 \\ 2x=360-200 \\ 2x=160 \\ x=(160)/(2) \\ x=80 \end{gathered}$

Thus,

Angle 3 = 80

Angle 6 = 80

Now,

Angle 3 and Angle 8 are corresponding angles. They are equal. Thus,

Angle 8 = 80

Angle 14 is vertical angle to angle 8. So, they are equal.

Angle 14 = 80

Angle 7 and Angle 8 are straight angles, they add to 180.

So,

$\begin{gathered} \angle7+\angle8=180 \\ \angle7+80=180 \\ \angle7=180-80 \\ \angle7=100 \end{gathered}$

Angle 7 = 100

Angle 13 is vertical angle to Angle 7, Thus, they are equal.

Angle 13 = 100

Angle 1 and Angle 9 are corresponding angles. They are equal. Hence,

Angle 9 = 60

Angle 11 is vertical angle to Angle 9. They are equal. Thus,

Angle 11 = 60

Angle 9 and Angle 10 fall in a straight line. They add to 180.

Thus,

$\begin{gathered} \angle9+\angle10=180 \\ 60+\angle10=180 \\ \angle10=180-60 \\ \angle10=120 \end{gathered}$

Angle 10 = 120

Angle 12 is vertical angle to angle 10. So, they are equal. Thus,

Angle 12 = 120

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Final Answers:

Angle 1 = 60

Angle 2 = 40 [given]

Angle 3 = 80

Angle 4 = 60 [given]