If the difference of the measures of two complementary angle is 120, then the angles will be A. 550, 350 B. 510, 390 C. 520, 380 D. none of these

We know, two angles are said to be complementary, if the sum of their measures is 90

∘

.

Let the angle be x

∘

and its complement is 90

∘

−x

∘

Then, according to the statement,

⇒x

∘

−(90

∘

−x

∘

)=12

∘

⇒x

∘

−90

∘

+x

∘

=12

∘

⇒2x

∘

=12

∘

+90

∘

=102

∘

⇒x

∘

=

2

102

∘

=51

∘

.

Hence, the measure of the angle is x=51

∘

and its complement is 90

o

−x=90

o

−51

o

=39

∘

.