Question

The support wire for a sign meets the wall and the overhang as shown below. If the measure of angle 2 is 42, find the measure of angle 1

Explain your reasoning plz

Answer 1

Hello!

The wall and the overhang meet to form a right angle, which we know to be an angle whose measure is equal to 90 degrees. Therefore, we can conclude that angles 1 and 2 are complementary angles. Complementary angles are two angles whose sum is equal to 90 degrees. This can be represented by the following formula:

A1 + A2 = 90

Insert any known values into the formula above:

A1 + 42 = 90

Subtract 42 from both sides of the equation:

A1 + 42 ( – 42 ) = 90 ( – 42 )
A1 = 48

We have now proven that Angle 1 is equal to 48 degrees.

I hope this helps!