7B - Angles at a Point, Real World Scenarios

Mason and Anika are studying geometry. They come across a diagram with two angles. They notice that these angles share a common vertex and a common side, but do not overlap. What term do Sophia, their tutor, use to describe these angles?

• Two angles that share a common vertex and overlap.

• Two angles that do not share a common vertex or side.

• Two angles that share a common side but not a common vertex.

• Two angles that share a common vertex and a common side, but do not overlap.

Answer explanation

The question asks about two specific angles that Mason and Anika are studying. These angles share a common vertex and a common side, but do not overlap. The correct term to describe these angles is 'adjacent angles'. The correct option is 'Two angles that share a common vertex and a common side, but do not overlap.' which accurately defines adjacent angles.

Aria and Ava are working on a project where they need to create a model of a door hinge. They notice that when the door is fully open, the two angles formed by the door and the wall are adjacent and their measures add up to 180 degrees. What type of angles are they creating?

• Vertical angles

• Complementary angles

• Supplementary angles

• Alternate interior angles

Answer explanation

In the question, Aria and Ava observe that the two angles created by the door and the wall add up to 180 degrees when the door is fully open. This characteristic defines Supplementary angles, which is the correct choice among the provided options. Supplementary angles are two angles whose measures add up to 180 degrees.

Abigail and Harper are working on a project where they need to create two adjacent angles using a protractor. They found that the measures of these two angles add up to 90 degrees. What type of angles have Abigail and Harper created?

• Complementary angles

• Alternate angles

• Vertical angles

• Supplementary angles

Answer explanation

In the question, it is stated that Abigail and Harper created two adjacent angles that add up to 90 degrees. Complementary angles are defined as two angles whose measures add up to 90 degrees. Therefore, the correct answer is 'Complementary angles'. The other options such as 'Alternate angles', 'Vertical angles' and 'Supplementary angles' do not meet the condition of adding up to 90 degrees.

Kai and Arjun are studying geometry. They come across a pair of angles and Kai says, 'These are complementary angles.' What does Kai mean by 'complementary angles'?

• Two angles whose sum is 270 degrees.

• Two angles whose sum is 90 degrees.

• Two angles whose sum is 45 degrees.

• Two angles whose sum is 180 degrees.

Answer explanation

In geometry, complementary angles are two angles whose measures add up to 90 degrees. So, when Kai says 'These are complementary angles', he means that the sum of the two angles is 90 degrees. This matches the correct choice: 'Two angles whose sum is 90 degrees'.

Hannah and Mia are studying geometry. They learned that two angles are complementary if their measures add up to 90 degrees. If Hannah measures one angle as 45 degrees, what would be the measure of the other angle that Mia needs to find to make them complementary?

• 30

• 180

• 45

• 90

Answer explanation

The question states that two angles are complementary if their measures add up to 90 degrees. Hannah has already measured one angle as 45 degrees. To find the other angle that would make them complementary, we would have to subtract Hannah's measure from 90. So, the other angle that Mia needs to find to make them complementary would be 90 - 45 = 45 degrees.

Kai and Evelyn are working on a project where they need to create a right angle using two smaller angles. Kai creates an angle of 60 degrees. How many degrees should the angle created by Evelyn be, so that the two angles are complementary?

• 45

• 75

• 30

• 90

Answer explanation

The question asks for the number of degrees needed so that two angles are complementary. Complementary angles are two angles that add up to 90 degrees. Since Kai's angle is 60 degrees, the angle needed by Evelyn to make a right angle would be 90 - 60 which is 30 degrees.

Rohan and Elijah are studying geometry. They come across a pair of angles and Rohan says, 'These are supplementary angles.' What does he mean by supplementary angles?

• Two angles that add up to 90 degrees.

• Two angles that add up to 180 degrees.

• Two angles that add up to 270 degrees.

• Two angles that add up to 360 degrees.

Answer explanation

In geometry, supplementary angles are two angles whose measures add up to 180 degrees. In the given question, Rohan is referring to this property of angles when he mentions 'supplementary angles'. The correct option, 'Two angles that add up to 180 degrees.', aligns with this definition of supplementary angles.

Maya and Liam are studying geometry. They learned that when two angles are supplementary, their measures add up to 180 degrees. If one of these angles measures 120 degrees, what would be the measure of the other angle?

• 60

• 180

• 90

• 30

Answer explanation

The question asks for the measure of the second angle if two angles are supplementary and one of them measures 120 degrees. Supplementary angles add up to 180 degrees. Hence, to find the measure of the other angle, we subtract the known angle from 180. Therefore, 180 - 120 equals 60 degrees which is the correct choice.

David and Grace are studying geometry. They learned that when two angles are supplementary, their measures add up to 180 degrees. If David measures one angle to be 150 degrees, what would be the measure of the other angle that Grace should find?

• 30

• 120

• 60

• 90

Answer explanation

In the question, we learn that David and Grace are studying geometry and that supplementary angles add up to 180 degrees. David has already found one angle to be 150 degrees. To find the measure of the other angle that Grace should find, we subtract David's measurement from 180. This gives us 30 degrees, which is the correct answer.

Aria and Arjun are studying geometry. They find two angles that are adjacent to each other and their measures add up to 90 degrees. William asks, are these angles also complementary?

• Sometimes.

• No

• Yes.

• It depends.

Answer explanation

Yes, the angles that Aria and Arjun found are complementary. In geometry, two angles are said to be complementary if their measures add up to 90 degrees. Since the two angles they found are adjacent and their measures add up to 90 degrees, they are indeed complementary.