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Answers
Answer:
(i) What is the value of x ?
Answer :- (b) 70°
Explanation :-
→ By linear pair ( 180° - 110° = 70° )
(ii) Δ APD and Δ BCQ are congruent by which criteria ?
Answer :- (b) SAS
Explanation :-
→ AD = BC (Given)
→ AP = CQ ( Opposite sides of a rectangle are equal )
→ \angle APD = \angle BQC∠APD=∠BQC (90° each)
\therefore∴ Δ APD ≈ Δ BCQ
(iii) PD is equal to which side ?
Answer :- (d) BQ
Explanation :-
→ By CPCT ( In Δ APD and Δ BCQ )
(iv) Δ ABC and Δ ACD are congruent by which criteria ?
Answer :- (a) SSS
Explanation :-
→ AB = CD (Given)
→ AD = BC (Given)
→ AC = AC (Common)
\therefore∴ Δ ABC ≈ Δ ACD
(v) What is the value of m ?
Answer :- (d) 20°
Explanation :
According to angle sum property of triangle,
\therefore \angle PAD + \angle ADP + \angle DPA = 180 \degree∴∠PAD+∠ADP+∠DPA=180°
\implies \angle m + 70 \degree + 90 \degree = 180\degree⟹∠m+70°+90°=180°
\implies \angle m + 160 \degree = 180 \degree⟹∠m+160°=180°
\implies \angle m = 180 \degree - 160 \degree⟹∠m=180°−160°
\implies \bf \angle m = 20 \degree⟹∠m=20°
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