The measure of A is 4 degrees greater than the measure of B. The two angles are complementary. Find the measure of each angle
angle B =X
angle A = x+4
complementary angles= 90 degrees
x+x+4= 90
2x= 86
x= 43 degrees for angle B
43+4 = 47 degrees for angle A
Hope this helps
Answer:
Two angles are said to be complementary angles if the sum of the measure of angles is 90 degree.
As per the statement:
The measure of A is 4 degrees greater than the measure of B
⇒\(m \angle A = 4^{\circ} + m\angle B\) .....[1]
It is given that: The two angles are complementary
By definition of complementary angles;
\(m \angle A+ m\angle B = 90^{\circ}\) .......[2]
Substitute equation [1] into [2] we have;
\(4^{\circ} + m\angle B + m\angle B =90^{\circ}\)
⇒\(4^{\circ} + 2 m\angle B =90^{\circ}\)
Subtract 4 degree from both sides we have;
\(2 m\angle B=86^{\circ}\)
Divide both sides by 2 we have';
\(m \angle B = 43\)
Substitute in [1] we have;
\(m \angle A = 4 + 43 = 47^{\circ}\)
Therefore, measure of each angles are:
\(m \angle A= 47\) and \(m \angle B = 43\)