Question

In MNO, the measure of angle O = 90^, OM = 1.8 feet, and NO = 4.1 feet. Find the measure of angle M to the nearest degree.

a) 23 ∘
b) 32 ∘
c) 57∘
d) 58 ∘

Answer 1

To find the measure of angle M in triangle MNO, we can use the concept that the sum of the angles in a triangle is always 180°. Since angle O is 90°, we can subtract that from 180° to find the sum of angles M and N. So, M + N = 180° - 90° = 90°. Next, we know that in a right triangle, the two acute angles (angles M and N) are complementary, which means they add up to 90°. Since we already know the sum of M and N is 90°, we can conclude that angle M is equal to angle N, which is 45°. Therefore, the measure of angle M to the nearest degree is 45°.

Step-by-step explanation:

To find the measure of angle M in triangle MNO, we can use the concept that the sum of the angles in a triangle is always 180°. Since angle O is 90°, we can subtract that from 180° to find the sum of angles M and N. So, M + N = 180° - 90° = 90°.

Next, we know that in a right triangle, the two acute angles (angles M and N) are complementary, which means they add up to 90°. Since we already know the sum of M and N is 90°, we can conclude that angle M is equal to angle N, which is 45°.

Therefore, the measure of angle M to the nearest degree is 45°.