Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?

Mathematics

2 answers:

topjm [15]3 years ago

7 0

Take -920/360 = -2.55555
Take the fraction part -0.5555555 * 360 = -200
The positive of that would be 160 degrees

Firlakuza [10]3 years ago

6 0

Answer: The required measure of angle D is 160°.

Step-by-step explanation: Given that angle D has a measure between 0° and 360° and is co terminal with an angle of measure –920°.

We are to find the measure of angle D.

We know that any two co terminal angles have measures that differ by a multiple of 360°.

So, to find the measure of angle D, we proceed as follows :

$-920^\circ+1\times360^\circ=-920^\circ+360^\circ=-560^\circ,\\\\-920^\circ+2\times360^\circ=-920^\circ+720^\circ=-200^\circ,\\\\-920^\circ+3\times360^\circ=-920^\circ+1080^\circ=160^\circ.$

Since 0° < 160° < 360°, so the required measure of angle D is 160°.

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