An angle is greater than 45o. Is its complementary angle greater than 45o or equal to 45o or less than 45o?

Solution

Let us assume the complementary angles be x and y,

We know that

The sum of measures of complementary angle pair is 90o.

Then,

= x + y = 90o

From the given details we get to know that

x > 45o

On adding y on both the sides,

= x + y > 45+ y

= 90o > 45+ y

= 90o – 45o > y

= y < 45o

Answer

Hence, its complementary angle is less than 45o.

Solution

Let us assume the complementary angles be x and y,

We know that

The sum of measures of complementary angle pair is 90o.

Then,

= x + y = 90o

From the given details we get to know that

x > 45o

On adding y on both the sides,

= x + y > 45+ y

= 90o > 45+ y

= 90o – 45o > y

= y < 45o

Answer

Hence, its complementary angle is less than 45o.

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