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Aneli [31]
3 years ago
13

Don’t understand what I’m supposed to do

Mathematics
2 answers:
chubhunter [2.5K]3 years ago
7 0

Answer:

139°

Step-by-step explanation:

supplementary angel means angel in a straight line

let angel qrs be X

41+X=180

X=180-41

X=139

Vladimir [108]3 years ago
4 0

Answer:

139 degrees

Step-by-step explanation:

Supplementary angles mean that the sum of the two angles should add up to 180 degrees. Since one of the angles is given, 41 degrees, and you know that the sum should be 180 degrees, you are able to find the measure of the unknown angle QRS.

41 + QRS = 180

QRS = 139 degrees

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Part 1

Focus on triangle ABC.

Since AB is a diameter of the circle, this means angle ACB is 90 degrees. Refer to Thale's Theorem. Or you could use the inscribed angle theorem. Thale's theorem is a special case of the inscribed angle theorem.

Minor arc CB is 48 degrees. Use the inscribed angle theorem to see that angle CAB is 48/2 = 24 degrees.

Therefore, angle CBA = 90 - (angle CAB) = 90 - 24 = 66 degrees

<h3>Answer: 66</h3>

========================================================

Part 2

Inscribed angle CBA was found to be 66 degrees back in part 1.

This doubles to 132 degrees to represent minor arc AC.

Or you could note that:

minor arc AC = 180 - (minor arc CB) = 180 - 48 = 132

Inscribed angle BCD is 48 degrees. This doubles to 96 degrees when using the inscribed angle theorem, and this is the measure of minor arc CBD.

-----------

Here's what we know about the arc measures of the circle

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  • minor arc CB = 48 degrees
  • minor arc BD = 96 degrees

These three arcs, along with minor arc AD, will add up to get a full 360 degree circle. Check out the diagram below.

Adding those 3 pieces gets us 132+48+96 = 276

This means minor arc AD has to be 360 - 276 = 84 degrees

Then use the inscribed angle theorem one more time to divide the minor arc AD in half to get the inscribed angle ACD

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