∠aangle, a and \angle b∠bangle, b are complementary angles. \angle a∠aangle, a measures 22^\circ22 ∘ 22, degrees. What is the measure of \angle b∠bangle, b?

The measure of angle ∠ b is 68°.

Step-by-step explanation:

There are two angles ∠ a and ∠ b which are complementary.

Therefore, from the definition of complementary angles, we have

∠ a + ∠ b = 90°

Now, if the angle ∠ a is measured to be 22°, then

22° + ∠ b = 90°

⇒ ∠ b = 90° - 22°

⇒ ∠ b = 68°

Therefore, the measure of angle ∠ b is 68°. (Answer)

0 and 5 minutes

step-by-step explanation:

given that one morning eight buses arrive late by the number of minutes given below:

0 8 2 6 9 2 0 7 8

write these in ascending order

0   0 2 6 7 8 8 9

in the afternoon two more buses arrive at the bus stop say by x and y minutes late.

total number of buses = 10

median = average of 4th and 5th after arranging in ascending order

since 4th entry is 6, the values of x and y should be below 6

also given 0 is the mode so either x or y or both should be 0 because then only 0 gets the maximum frequency and hence mode

thus we have

0 0 0 2 6 7 8 8 9 and another unknown entry which is below 6.

since median is 3.5, we have the unknown entry to be 5 only because then only median =( 2+5)/2

thus the after noon buses were late by 0 and 5 minutes.