Question 2

The measures of two supplementary angles are in the ratio of 2: 3. Find the measurements of the two angles.

Question 3

In a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle. Find the measurements of the two angles.

1) m∠ 1 = 72°, m∠2 = 108°,

2) m∠ 1 = 22.5°, m∠2 = 67.5°

Step-by-step explanation:

Question 2) Assuming these are supplementary angles, we know that their measures form a linear pair that add to 180°;

let us assign these angles as 1, and 2 ⇒ m∠ 1 + m∠ 2 = 180,

with the given ratios 2 to 3, we can say x ⇒ one part of measure, so that ⇒ 2x + 3x = 180,

2x + 3x = 180 ⇒ combine like terms,

5x = 180 ⇒ divide either side by 5,

x = 36°

If this is so, m∠ 1 = 2x = 2 * (36) = 72°, and m∠ 2 = 3x = 3 * (36) = 108°;

Solution; m∠ 1 = 72°, m∠2 = 108°

Question 3) If it is known that two angles are complementary to one another, we can say their measures add to 90°;

let us one more, assign these angles as 1 and 2 ⇒ m∠ 1 + m∠ 2 = 180,

knowing that the measure of one angle is 3 times that of the other angle we can derive the ratio 1 : 3 in the manner smaller ∠ measure : bigger ∠ measure so that ⇒ x + 3x = 90,

x + 3x = 90 ⇒ combine like terms,

4x = 90 ⇒ divide either side by 4,

x = 22.5

If this is so, m∠ 1 = x = 1 * (22.5) = 22.5°, and m∠ 2 = 3x = 3 * (22.5) = 67.5°;

Solution; m∠ 1 = 22.5°, m∠2 = 67.5°