Question

angles
a vertex is a point where two rays or line - segments intersect. an angle is formed by two rays. the rays that form an angle are called the sides of the angle.
the size of an angle depends on the amount of rotation of the sides. imagine a clock with both hands pointing at the 12. as one hand moves clockwise, the measure of the angle created by the hands increases. angles are measured in degrees (°). one full rotation (forming a complete circle) is 360°.
below are the properties of four angles that you will need to know.
name of angle properties examples
tright angle exactly 90°
acute angle less than 90°
straight angle exactly 180°
obtuse angle between 90° and 180°
answer each question.

1. match the illustrations with the descriptions.

_____ an acute angle
_____ a right angle
_____ an obtuse angle
_____ a straight angle

1. which of the three angles is smallest? why? (hint: the size of an angle is based only on the angle, not the length of the sides.)

Explanation:

Step1: Recall angle - type definitions

An acute angle is less than 90°, a right - angle is 90° (marked by a small box), an obtuse angle is between 90° and 180°, and a straight angle is 180°.

Step2: Match illustrations to definitions

• For an acute angle, illustration d has an angle less than 90°.
• For a right - angle, illustration c has a small box indicating 90°.
• For an obtuse angle, illustration b has an angle between 90° and 180°.
• For a straight angle, illustration a is a straight line representing 180°.

Step3: Determine the smallest of three angles

Among the three angles in the second part (a is acute, b is right, c is obtuse), since an acute angle is less than 90°, a right - angle is 90°, and an obtuse angle is greater than 90°, angle a is the smallest.

Answer:

1. d. an acute angle

c. a right angle
b. an obtuse angle
a. a straight angle

1. Angle a is the smallest because it is an acute angle (less than 90°), while angle b is a right - angle (90°) and angle c is an obtuse angle (greater than 90°).