Question 196

The measures of two angles of a triangle are in the ratio 4 : 5. If the sum of these two measures is equal to the measure of the third angle, find the smallest angle.

Solution

Let the two angles of the triangle be 4$$\theta$$ and 5$$\theta$$

=> Third angle = 180° - (4$$\theta$$+5$$\theta$$) = 180° - 9$$\theta$$

Acc to ques :

=> 4$$\theta$$ + 5$$\theta$$ = 180° - 9$$\theta$$

=> 18$$\theta$$ = 180°

=> $$\theta$$ = 10°

=> Smallest angle = 4$$\theta$$

= 4*10 = 40°

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