Question

∠A and ∠B are complementary angles. if m∠A =(3x+23) and∠B=3x+25) then find the measure of ∠B

Answer 1

Explanation:

If two angles are complementary, then their sum is 90°.

So we can build an equation using this information.

The angles are 3x + 23 and 3x + 25, respectively.

`\bf{3x+23+3x+25=90}`

Combine the like terms

`\bf{6x+48=90}`

Now just solve for x

`\bf{6x=90-48}`

`\bf{6x=42}`

`\bf{x=7}`

Knowing that x = 7, we can plug it into the expressions

3x + 25

3(7) + 25

21 + 25

46

Now the other angle is:

3x + 23

3(1) + 23

21 + 23

44

Hence, the measures of
`\angle A` and
`\angle B` are 44 and 46, respectively.