1.

In a quadrilateral, angles A, B, C are in the ratio 4:2:5 and fourth angle is 140 degree, then the measure of smallest angle is​

Answer»

Given :-

  • Angles GIVEN in the ratio = 4 : 2 : 5
  • Fourth angle = 140°

To find :-

  • Measure of the smallest angle = ?

Solution :-

LET the angles given in the ratio be :-

  • Sum of the angles of quadrilateral = 360°

\mapsto 4x + 2x + 5x + 140° = 360°

\mapsto 11x + 140° = 360°

\mapsto 11x = 360° - 140°

\mapsto 11x = 220°

\mapsto \sf{x~=~\dfrac{220 \degree}{11}}

\mapsto \sf{x~=~20 \degree}

  • The value of x = 20°

\mapsto Measure of all the angles :-

  • 4x = 4 × 20° = 80°
  • 2x = 2 × 20° = 40°
  • 5x = 5 × 20° = 100°
  • Fourth angle = 140° (given)

The smallest angle \mapsto 40°


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