The measure of angle A is 124 degrees. What is the correct classification for angle A?
A. acute
B. right
C. obtuse
D. straight
Find the complement of an angle with a measure of 72 degrees
A. 162 degrees
B. 18 degrees
C. 252 degrees
D. 108 degrees
The measure of two angles of a triangle are 36 degrees and 71 degrees. Find the measure of the third angle and classify the triangle according to its angles.
A. 199 degrees, acute
B. 199 degrees, right
C. 73 degrees, acute
D. 73 degrees, right
Ms. Sue you said you'd check their answers, not make them feel bad about themselves.
1. C, as any angle greater than 90 degrees is obtuse (unless it's a straight angle measuring 180 degrees)
2. B, as a complement of an angle means it, added to the given angle, would be 90 degrees (A supplement would be the same just for 180 degrees)
3. C, as we know that all angles in a triangle added together is 180 degrees, and 180-36-71 is 73. And since all three angles are acute in this triangle, the triangle is acute.
To determine the correct classification for angle A, we need to compare its measure to the definitions of different types of angles:
1. Acute angles: These are angles that measure less than 90 degrees.
2. Right angles: These are angles that measure exactly 90 degrees.
3. Obtuse angles: These are angles that measure between 90 and 180 degrees.
4. Straight angles: These are angles that measure exactly 180 degrees.
Since angle A measures 124 degrees, it falls into the category of Obtuse angles (C).
To find the complement of an angle with a measure of 72 degrees, we need to subtract the given angle measure from 90 degrees. Complementary angles add up to 90 degrees.
Complement = 90 degrees - 72 degrees = 18 degrees
Therefore, the complement of an angle with a measure of 72 degrees is 18 degrees (B).
In a triangle, the sum of all three angles is always 180 degrees. Therefore, to find the measure of the third angle, we subtract the sum of the two known angles: 180 degrees - (36 degrees + 71 degrees) = 73 degrees.
The measure of the third angle is 73 degrees. Now, let's classify the triangle based on its angles:
1. Acute triangle: All three angles in the triangle are less than 90 degrees.
2. Right triangle: One angle in the triangle measures exactly 90 degrees.
3. Obtuse triangle: One angle in the triangle measures more than 90 degrees.
Since all three angles in the triangle have measures less than 90 degrees, the triangle is classified as an acute triangle. Therefore, the correct answer is (C) 73 degrees, acute.