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The measure of A is 4 degrees greater than the measure of B. The two angles are complementary. Find the measure of each angle

Sagot :

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

⇒[tex]m \angle A = 4^{\circ} + m\angle B[/tex]       .....[1]

It is given that:  The two angles are complementary

By definition of complementary angles;

[tex]m \angle A+ m\angle B = 90^{\circ}[/tex]       .......[2]

Substitute equation [1] into [2] we have;

[tex]4^{\circ} + m\angle B + m\angle B =90^{\circ}[/tex]

⇒[tex]4^{\circ} + 2 m\angle B =90^{\circ}[/tex]

Subtract 4 degree from both sides we have;

[tex]2 m\angle B=86^{\circ}[/tex]

Divide both sides by 2 we have';

[tex]m \angle B = 43[/tex]

Substitute in [1] we have;

[tex]m \angle A = 4 + 43 = 47^{\circ}[/tex]

Therefore, measure of each angles are:

[tex]m \angle A= 47[/tex] and [tex]m \angle B = 43[/tex]