Question

Three angles of a quadrilateral are in the ratio 1:2:3. The sum of the smallest and the greatest of these angles is equal to 180°. Find all the angles of the quadrilateral.​

Answer 1

Answer:

We have, sum of smallest angle and greatest angle is 180 degree. Sum of all angles of quadrilateral is 360°. So four angles of quadrilateral are 45°, 90°, 90° and 135°

Step-by-step explanation:

hope it helps you

Answer 2

Dear Student,

● Answer -

45°, 90°, 90° and 135°

◆ Explanation -

Given that 3 angles are in ratio 1:2:3. Let x be common multiple such that angles become x, 2x and 3x.

We have, sum of smallest angle and greatest angle is 180 degree.

x + 3x = 180°

4x = 180°

x = 180°/4

x = 45°

These 3 angles become,

x = 45°

2x = 2×45 = 90°

3x = 3×45 = 135°

Sum of all angles of quadrilateral is 360°.

45° + 90° + 135° + 4th angle = 360°

270° + 4th angle = 360°

4th angle = 360° - 270°

4th angle = 90°

So four angles of quadrilateral are 45°, 90°, 90° and 135°.

Hope this helps you...