Question

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?

Answer 1

(i) Yes

Two acute angles he complement to each other.
Example: ${35}^{\circ }+{55}^{\circ }={90}^{\circ }$
(ii) No

Since two obtuse angles will each be greater than ${90}^{\circ }$, they cannot be complementary to each other.
(iii) No.
Since two right angles will each be equal to ${90}^{\circ }$, they cannot be complement to each other.
(iv) No.
Since the sum of two acute angles is always less than ${180}^{\circ }$, they cannot be supplement to each other.
(v) No.
Since the sum of two obtuse angles is always greater than ${180}^{\circ }$, they cannot be supplementary to each other.
(vi) Yes.
Since the sum of two right angles is ${180}^{\circ }$.

(i.e., ${90}^{\circ }+{90}^{\circ })$, they are supplementary to each other.
(vii) Yes.

(viii) Yes.

(ix) Yes.

(x) Yes.

(xi) No.
If one angle in a linear pair is acute, then the other angle would be obtuse.

(xii) No.
If one angle in a linear pair is obtuse, the other angle would be acute.

(xiii) Yes.