Two acute angles cannot form a pair of supplementary angles. Justify.

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Solution

By definition, acute angles are the angles that measure the angle greater than $0 °$ and less than $90 °$ . If you add two acute angles in which each angle is large as possible, its sum will be less than $180 °$ . By the definition of supplementary angles, it is impossible to get the supplementary angle when we add two acute angles.
Example: $80 ° + 60 ° = 140 °$ which is not a supplementary angle.
But, in the case, if we add more than two acute angles, we can get supplementary angles.

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Similar questions

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 85

Can two acute angles form a pair of supplementary angles? Give reason in support of your answer.

Which of the following statements are true., (T) and which are false (F)?

(i) Angles forming a linear pair are supplementary.
(ii) If two adjacent angles are equal, then each angle measures $90^{\circ}$ .
(iii) Angles forming a linear pair can both be acute angles.
(iv) If angles forming a linear pair are equal, then each of these angles is of measure $90^{\circ}$ .

Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is _______.

(iii) Two angles forming a linear pair are _______.

(iv) If two adjacent angles are supplementary, they form a _______.

(v) If two lines intersect at a point, then the vertically opposite angles are always _______.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _______.

Q. Two acute angles cannot form a pair of supplementary angles . Justify .

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