If two adjacent angles are supplementary, they form a ___________.

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Solution

Define linear pair with figure
We know that the sum of measures of a pair of supplementary angles is $180 °$ .
From the figure we can see that $∠ D B A$ and $∠ D B C$ are adjacent angles.
$∠ D B A$ and $∠ D B C$ form a line $A C$ or line $D B$ intersects line $A C$ at point $B$ .
The angle measured on a straight line is equal to $180 °$
Thus $∠ D B A$ and $∠ D B C$ are adjacent supplementary angles.
Linear pair of angles are formed when two lines intersect each other at a single point or at a common point of intersection.
Hence, two adjacent supplementary angles form a linear pair.

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Similar questions

Question 13 (iv)
If two adjacent angles are supplementary, they form a ___

Question 2

$Δ D E F$ in the given figure is a right-angled triangle with $∠ E = 90^{\circ}$ . What type of angles are $∠ D$ and $∠ F$ ?

a) They are equal angles
b) They form a pair of adjacent angles
c) They are complementary angles
d) They are supplementary angles

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. Construct the following figures.
(i) A pair of adjacent angles
(ii) Two supplementary angles which are not adjacent angles.
(iii) A pair of adjacent complementary angles.

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?

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