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Question
Construct a ∆ PQR such that:
PR = 5.8 cm, ∠P = 60° and ∠R = 45°. Measure ∠Q and verify it by calculations
Solution
Steps of Construction :
(i) Draw a line segment PR = 5.8 cm
(ii) At P, construct an angle of 60°
(iii) At R, draw another angle of 45° meeting each other at Q.
∆ PQR is the required triangle. On measuring ∠Q, it is 75°
Verification: We know that sum of angles of a triangle is 180°
∴∠P + ∠Q + ∠R = 180°
⇒ 60° + ∠Q + 45° = 180°
⇒ ∠Q + 105° = 180°
⇒ ∠Q = 180° – 105° = 75°.
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