Fill in the blanks so as to make the following statements true:

(i) If one angle of a linear pair is acute, then its other angle will be ........
(ii) A ray stands on a line, then the sum of the two adjacent angles so formed is ..........
(iii) If the sum of two adjacent angles is 180°, then the ........ arms of the two angles are opposite rays.

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Solution

(i)

If one angle of a linear pair be acute, then its other angle will be obtuse.

Explanation:

Let us assume one of the angle in a linear pair be; such that,that is, an acute angle.

Therefore, the other angle in the linear pair becomes, which clearly cannot be acute.

(ii)

A ray stands on a line, and then the sum of the two adjacent angles so formed is.

Explanation:

The statement talks about two adjacent angles forming a linear pair.

(iii) If the sum of the two adjacent angles is, then the uncommon arms of the two angles are opposite rays.

Explanation:

The statement talks about two adjacent angles forming a linear pair.

Therefore, this can be drawn diagrammatically as:

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Similar questions

Fill in the blanks so as to make the following statements true:
(i) If one angle of a linear pair is acute, then its other angle will be___.
(ii) A ray stands on a line, then the sum of the two adjacent angles so formed is ___.
(iii) If the sum of two adjacent angles is $180^{\circ}$ , then the ___ arms of the two angles are opposite rays.

Q. If a ray stands on a line, then sum of two adjacent angles so formed is:

Q. Read the following two statements which are taken as axioms :
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to

180^{o}

.
Is this system of axioms consistent?

A ray stands on a line, then the sum of the two adjacent angles so formed is_______.

Q. A ray stands on a line, then the sum of the two adjacent angles so formed is ______.

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