Question 1

Given the diagram, the angles around a point sum to $$360^	ext{o}. If $$the known angles are $$110^	ext{o}$$, $$65^	ext{o}$$, and $$20^	ext{o}$$, what is the value of $$a^	ext{o}$$?

Accepted Answer

$$a = 55$$

Question 2

If $$a^	ext{o}$$, $$b^	ext{o}$$, $$c^	ext{o}$$, $$110^	ext{o}$$, $$65^	ext{o}$$, and $$20^	ext{o}$$ are angles around a point, and $$a = 55^	ext{o}$$, $$b = 65^	ext{o}$$, $$c = 110^	ext{o}$$, which equation correctly represents the sum of all angles?

Accepted Answer

$$a + b + c + 110 + 65 + 20 = 360$$

Question 3

What is the value of $$b^	ext{o} in $$the diagram, given the sum of all angles around a point is $$360^	ext{o}$$ and the other angles are $$110^	ext{o}$$, $$65^	ext{o}$$, $$20^	ext{o}$$, and $$a^	ext{o} = 55^	ext{o}$$?

Accepted Answer

$$b = 65$$

Question 4

If $$c^	ext{o} is $$the remaining unknown angle and the other angles are $$110^	ext{o}$$, $$65^	ext{o}$$, $$20^	ext{o}$$, $$a^	ext{o} = 55^	ext{o}$$, and $$b^	ext{o} = 65^	ext{o}$$, what is the value of $$c^	ext{o}$$?

Accepted Answer

$$c = 110$$

Question 5

Which of the following best describes the process to solve for $$a$$, $$b$$, and $$c in $$the diagram?

Accepted Answer

Subtract the sum of the known angles from $$360 to $$find the sum of $$a$$, $$b$$, and $$c$$, then assign values based on the diagram.

Question 6

If the sum of all angles around a point is $$360^	ext{o}$$, and the known angles are $$110^	ext{o}$$, $$65^	ext{o}$$, and $$20^	ext{o}$$, what is the sum of the unknown angles $$a^	ext{o}$$, $$b^	ext{o}$$, and $$c^	ext{o}$$?

Accepted Answer

$$a + b + c = 165$$

Question 7

If $$a^	ext{o}$$, $$b^	ext{o}$$, and $$c^	ext{o}$$ are consecutive angles and their sum is $$165^	ext{o}$$, which of the following could be a possible set of values for $$a$$, $$b$$, and $$c$$?

Accepted Answer

Question 8

If the sum of the angles around a point is $$360^	ext{o}$$, and you know three of the angles ($$110^	ext{o}$$, $$65^	ext{o}$$, $$20^	ext{o}$$), what is the equation to find the sum of the remaining angles?

Accepted Answer

$$360 - (110 + 65 + 20)$$

Question 9

If you are given the angles $$110^	ext{o}$$, $$65^	ext{o}$$, $$20^	ext{o}$$, and $$a^	ext{o} = 55^	ext{o}$$, what is the sum of these four angles?

Accepted Answer

$$250$$

Question 10

If the sum of all angles around a point is $$360^	ext{o}$$, and you know $$110^	ext{o}$$, $$65^	ext{o}$$, $$20^	ext{o}$$, and $$a^	ext{o} = 55^	ext{o}$$, what is the sum of the remaining angles?

Accepted Answer

$$110$$

Finding Unknown Angles Around a Point

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