Page 3 - WSA

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We know that the sum of the angles of a triangle is 180 .
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∴ ∠PQR + ∠QRP + ∠RPQ = 180
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= 105 + 40 + ∠RPQ = 180
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= 145 + ∠RPQ = 180
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= ∠RPQ = 180 – 145
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= ∠RPQ = 35
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Hence, the measures of ∠RPQ is 35 .
Steps of construction:

1. Draw a line segment PQ = 5 cm.
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2. At point P, draw a ray L to making an angle of 105 i.e. ∠LPQ = 35 .
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3. At point Q, draw a ray M to making an angle of 40 i.e. ∠MQP = 105 .
4. Now the two rays PL and QM intersect at the point R.

Then, ΔPQR is the required triangle.

6. Solution:-

Steps of construction:

1. Draw a line segment BC = 6 cm.
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2. At point C, draw a ray CX to making an angle of 90 i.e. ∠XCB = 90 .
3. With C as a center and radius 6 cm, draw an arc that cuts the ray CX at A.
4. Join AB.

Then, ΔABC is the required right angled triangle.

7. Solution: