Question

Ray PQ and ray PR are perpendicular to each other. Points B and A are in the interior
and exterior of QPR respectively. Ray PB and ray PA are perpendicular to each other
Draw a figure showing all these rays and write -
(1) A pair of complementary angles (ii) A pair of supplementary angles.
(mm) A pair of congruent angles​

Answer 1

Ray PQ and PRare perpendicular each other. Point B is the interior and Point A is the exterior of ∠QPR.

Ray PB and PA are perpendicular to each other.

(i) A pair of Complementary angles:

⇒ ∠QPB and ∠BPR because their sum is 90

o

⇒ ∠BPR and ∠RPA because their sum is 90

o

(ii) A pair of Supplementary angles:

⇒ ∠QPR and ∠BPA because their sum is 180

o

(iii) A pair of congruent angles:

⇒ ∠BPA≡∠QPR [ Each angle is 90

o

]

⇒ ∠BPA=∠QPR

So, ∠RPA+∠BPR=∠BPR+∠QPB [ Using angle addition property ]

So, ∠RPA=∠QPB

Hence, ∠RPA≡∠QPB