What is the value of m∠1 to be if ∠1 and ∠2 are complementary angles and m∠2=85° ?
Complementary angles add up to 90 degrees. Since ∠1 and ∠2 are complementary angles and ∠2 is given to be 85 degrees, we can find the value of ∠1 by subtracting ∠2 from 90 degrees.
∠1 = 90° - ∠2 = 90° - 85° = 5°
A figure consists of four angles. The angle measures are as follows: m∠1=65°, m∠2=90°, m∠3=30°, and m∠4=25°. Which two angles are complementary angles? Identify by the angle number and not the degree measurement. List the smaller angle value first and the larger angle value second.
Two angles are considered complementary if their measures add up to 90 degrees.
To determine which two angles are complementary, we need to check all possible pairs of angles and see if their measures add up to 90 degrees.
Checking all pairs:
∠1 and ∠2: m∠1 + m∠2 = 65° + 90° = 155° (not complementary)
∠1 and ∠3: m∠1 + m∠3 = 65° + 30° = 95° (not complementary)
∠1 and ∠4: m∠1 + m∠4 = 65° + 25° = 90° (complementary)
∠2 and ∠3: m∠2 + m∠3 = 90° + 30° = 120° (not complementary)
∠2 and ∠4: m∠2 + m∠4 = 90° + 25° = 115° (not complementary)
∠3 and ∠4: m∠3 + m∠4 = 30° + 25° = 55° (not complementary)
Therefore, angles ∠1 and ∠4 are complementary angles.