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Which of these are the measures of angles 1, 2, and 3?

Updated: 4/28/2022
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monique robles

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monique robles

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Q: Which of these are the measures of angles 1, 2, and 3?
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Two complementary angles have measures in the ratio 2 to 3 what are their measures?

The sum of two complementary angles is 90°.If the ratio is 2:3 then there are 5 parts in total.90 ÷ 5 = 18.The angles measure 2 x 18 = 36° and 3 x 18 = 54°.


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Do you mean "Are two vertical angles always congruent?" Vertical angles are always congruent, but congruent angles do not have to be vertical. Any two angles with the same angle measurement are considered congruent by definition. The reason why vertical angles are always congruent is explained below. Imagine (or draw) an X forming 2 pairs of vertical angles. ∠1 is to the left, ∠2 is on top, ∠3 is to the right, and ∠4 is on the bottom. Vertical angles are always congruent because ∠1 and ∠2 are supplementary, meaning that their measures add to 180 degrees. The measures of ∠2 and ∠3 also add to 180 degrees. This means that m∠1+m∠2=180 and m∠2+m∠3=180. Using the Transitive Property, it becomes m∠1+m∠2=m∠2+m∠3. If you subtract the measure of ∠2 from both sides, it becomes m∠1=m∠3. I hope that helped!


If measures of 3 supplementary angles are in the ratio 1 to 3 to 2 what are the values of the angles?

call the small angle x, then given the ratios we have x+2x+3x=180 6x=180 so x=30 The angles are 30, 60, and 90.


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Can you write a two column proof given angles 2 and 3 are congruent and prove angles 1 and 4 are congruent?

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The angle measures are 59, 60 and 61. Use algebra to figure this out. Let x = the first consecutive number, x + 1 the second and x + 2 the third. So you have x + x + 1 + x + 2 = 180 3x + 3 = 180 3x = 177 x = 59


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