Suppose that angle COP and angle TOD are vertical angles, the measure of angle COP is 11x-17 and The measure of angle TOD is 9x+

Question

2 years ago

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Suppose that angle COP and angle TOD are vertical angles, the measure of angle COP is 11x-17 and The measure of angle TOD is 9x+

11.
Part A: construct angle COP and angle TOD [Hint: angle COD is an adjacent angle to angle COP and angle POT is an adjacent angle to angle TOD.]

Part B: determine the measure of angle COD and the measure of angle POT.

Mathematics

1 answer:

crimeas [40] · Answer 1 · 2022-10-29T02:01:13+03:00

The measure of <COD and <POT are 43 and 43degrees respectively

The point where two lines meet or intersect is known as an angle:

Is <COP and angle TOD are vertical angles, this means that they are equal i.e.

<COP = <TOD

Given that:

<COP = 11x - 17

<TOD = 9x + 11

Equate both expressions

11x - 17 = 9x + 11

11x - 9x = 11 + 17

2x = 28

x = 28/2

x = 14

Get <COP

<COP = 11x - 17

<COP = 11(14) - 17

<COP = 154-17

<COP = 137 degrees

Since <COP = <TOD, hence <TOD = 137 degrees

Calculate <COD:

<COD + <TOD = 180

<COD + 137 = 180

<COD = 180 - 137

<COD = 43 degrees

Also <POT = <COD = 43degrees(vertically opposite angles)

Hence the measure of <COD and <POT are 43 and 43degrees respectively

Learn more here: brainly.com/question/17247176