if triangle ABC is congruent to triangle QRPand angle A=60', angle B=45' then P=? (a)45',(b)=60',(c)105' (d)=75'
Answers
Given:
ΔABC ≡ ΔQRP
∠A = 60°
∠B = 45°
To find:
The value of ∠P
Calculation:
As both the triangles are congruent, the respective angles in both the traingles will be equal i.e.,
∠Q = ∠A = 60°
∠R = ∠B = 45°
∠P = ∠C
The sum of angles in a triangle is equal to 180°. In ΔQRP
=> ∠Q+∠R+∠P = 180°
60°+ 45°+∠P = 180°
105° + ∠P = 180°
∠P = 75°
The value of ∠P is 75° [option(d)]
Answer: (d) is the correct option. The value of ∠P is 75°
Step-by-step explanation:
We have , ΔABC ≡ ΔQRP
∠A = 60° and ∠B = 45°
As per the Congruency theorem, Congruent triangles are those two triangles having corresponding sides and angles equal. Congruence is depicted by the symbol ≅. They also have the same area and the same perimeter.
Therefore, in ΔQRP,
∠Q = ∠A = 60°
∠R = ∠B = 45°
∠P = ∠C
The sum of angles in a triangle is always equal to 180°.
In ΔQRP, ∠Q+∠R+∠P = 180°
Putting the values of angle Q=60', angle R=45, we get
60°+ 45°+∠P = 180°
105° + ∠P = 180°
∠P = 75°
Hence, ∠P = 75°
Hope it helps!
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