the difference in the measure of two complementary angles is 12 find the measure of the angles of 51 and 49
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Answer:
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
∘
.
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