Question

The angles are supplementary and the smaller is one-half of the larger.
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Answer 1

Answer:

let the larger angle be x then the smaller will be 1x

2

ATQ

x+1x =180°

2

2x+x =180°

2

3x =180°×2

3x=360°

x=360°

3

x=120°( larger angle)

Smaller angle =1x =120° =60°

2 2

Answer 2

Answer:

They are called Supplementary angles.

Explanation:

Two Angles are Supplementary when they add up to 180 degrees. They don't have to be next to each other, just so long as the total is 180 degrees. Examples: 60° and 120° are supplementary angles.

One of its angles is acute angle and another angle is an obtuse angle

Both of the angles are right angles.

This means that ∠A + ∠B = 180°.

Two angles have a sum of 180°

∠A + ∠B = 180°.

Supplementary angles form a straight line.

PROPERTIES OF SUPPLEMENTARY ANGLES.

The important properties of supplementary angles are:

The two angles are said to be supplementary angles when they add up to 180°.

The two angles together make a straight line, but the angles don’t have to be together.

“S” of supplementary angle stands for “Straight” line. This means that it forms 180°.

How to Find Supplementary Angles?

For example, if you had given that two angles form supplementary angles and you are provided with one angle and asked to find the other angle, you can easily find the other angle using the formula

∠A = 180° – ∠B (or)

∠B = 180° – ∠A

Adjacent and Non-Adjacent Supplementary Angles

The supplementary angles may be classified as either adjacent or nonadjacent. The adjacent supplementary angle shares the line segment or arm with each other whereas the non-adjacent supplementary angles do not share the line segment or arm.

Supplementary Angles Theorem

The supplementary angle theorem states that if two angles are said to be supplementary to the same angle, then the two angles are said to be congruent.

Supplementary Angles Examples

Some of the examples of supplementary angles are

120° + 60° = 180°

90° + 90° = 180°

140° + 40° =180°

96° + 84° =180°

Can 2 Acute Angles be Supplementary Angles?

No, two acute angles cannot form a supplementary angle.

By definition, acute angles are the angles that measure the angle greater than 0° and less than 90°. If you add two acute angles in which each angle is large as possible, its sum will be less than 180°. By the definition of supplementary angles, it is impossible to get the supplementary angles when we add two angles.

Example: 80° +60° = 140° which is not a supplementary angle.

But, in the case, if we add more than two acute angles, we can get supplementary angles.

Can 2 Obtuse Angles be Supplementary Angles?

No, two obtuse angles cannot form a supplementary angle.

By the definition of obtuse angles,  the angles that measure the angle greater than 90°. If you add two obtuse angles, the sum will be greater than 180°. It will not satisfy the property of the supplementary angle when we add obtuse angles.

Example: 110° + 95° = 205° which is not a supplementary angle. [205° >180° ]

But, in the case, if we add more than two acute angles, we can get supplementary angles.

Can 2 Right Angles be Supplementary Angles?

Yes, 2 right angles can form a supplementary angle. We know that when the measure of an angle is exactly 90°, then it is known as a right angle.

When two right angles are added, it is possible to get the supplementary angle. because 90° + 90° = 180°, as it satisfies the condition of supplementary angle.

Supplementary Angles problem

Question:

Find the measure of unknown angle from the given figure.

Solution:

We know that the supplementary angle sum up to 180°

X + 55° + 40° = 180°

X + 95° = 180°

X = 180°- 95°

X = 85°

Therefore, the unknown angle, X = 85°