Angles x and y form a pair of complementary angles. Can x or y be an obtuse angle? Answer in Yes/No.

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Solution

The measure of a pair of complementary angles adds up to $90^{o} .$
The pair of complementary angles are $x$ and $y .$

$∴ x + y = 90^{o}$

Hence, $x$ and $y$ must be less than $90^{o}$ or equal to $90^{o}$ (not both at a time).

$∴ x$ and $y$ cannot be an obtuse angle.

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Answer the following questions and justify.
(i) Can two acute angles he complement to each other?
(ii) Can two obtuse angles be complement to each other?
(iii) Can two right angles he complement to each other?
(iv) Can two acute angles be supplementary?
(v) Can two obtuse angles be supplementary?
(vi) Can two right angles be supplementary?
(vii) Can two adjacent angles be supplementary?
(viii) Can two adjacent angles be complementary?
(ix) Can two obtuse angles be adjacent angles?
(x) Can an acute angle be adjacent to an obtuse angle?
(xi) Can two acute angles form a linear pair?
(xii) can two obtuse angles form a linear pair?
(xiii) Can two right angles form a linear pair?

Question 58

State whether the statement is True or False.

One obtuse angle and one acute angle can make a pair of complementary angles

Q. Can there be a pair of complementary angles such that both of them are equal? If yes, find the values of those angles.

In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles

(ii) Adjacent complementary angles

(iii) Equal supplementary angles

(iv) Unequal supplementary angles

(v) Adjacent angles that do not form a linear pair

Sunita knows that the sum of complementary angles is equal to $90^{\circ}$ . She thinks that there can be a pair of complementary angles such that both of them are equal. Is she correct? If yes, then find such a pair of angle.

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Angles x and y form a pair of complementary angles. Can x or y be an obtuse angle? Answer in Yes/No.

The measure of a pair of complementary angles adds up to 90o. The pair of complementary angles are x and y. ∴x+y=90o Hence, x and y must be less than 90o or equal to 90o (not both at a time). ∴x and y cannot be an obtuse angle.

The measure of a pair of complementary angles adds up to $90^{o} .$
The pair of complementary angles are $x$ and $y .$

$∴ x + y = 90^{o}$

Hence, $x$ and $y$ must be less than $90^{o}$ or equal to $90^{o}$ (not both at a time).

$∴ x$ and $y$ cannot be an obtuse angle.