Question

Three angles of the quadrilateral are in the ratio 1:2:3 and the sum of the smallest angle and the greatest angle is 180degree. Find the all angles of the quadrilateral

Answer 1

answer is 45:90:135
1x+3x=180
4x=180
x=180/4
x=45
1x
1×45
45

2×45
90

3×45
135

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...