Question 77

The angles in a triangle are in a ratio of 19 : 10 : 7. What is the sum of thrice the smallest angle and the twice the largest angle ?

Solution

Let the angles of the triangle be $$19x , 10x , 7x$$

=> Sum of angles = $$19x + 10x + 7x = 180^{\circ}$$

=> $$36x = 180^{\circ}$$

=> $$x = \frac{180}{36} = 5^{\circ}$$

=> Angles are = $$95^{\circ} , 50^{\circ} , 35^{\circ}$$

$$\therefore$$ Sum of thrice the smallest angle and the twice the largest angle

= $$(3 \times 35^{\circ}) + (2 \times 95^{\circ})$$

= $$105 + 190 = 295^{\circ}$$

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