The angles of a quadrilateral are in an arithmetic sequence. The large

1.	The angles of a quadrilateral are in an arithmetic sequence. The largest angle is 150°. Find other angles.
Answer» Sum of four angles of a quadrilateral = 360° Angles are in arithmetic sequence, so first angle + 3 x common difference (d) = 150° i.e., f + 3d = 150 The four angles are f, f + d, f + 2d, f + 3d. f + f + d + f + 2d + f + 3d = 360° f + f + d + f + 2d + 150 = 360° 3f + 3d = 360° - 150 = 210 3(f + d) = 210 f + d = \(\frac{210}{3}=70\) The four angles are f, 70, f + 2d, 150 . f + 2d = \(\frac{150+70}{2}=110\) Common difference = 110 – 70 = 40 First angle = 70 – 40 = 30 So, the four angles are 30, 70, 110, 150

The angles of a quadrilateral are in an arithmetic sequence. The largest angle is 150°. Find other angles.

Answer»

Sum of four angles of a quadrilateral = 360° Angles are in arithmetic sequence, so first angle + 3 x common difference (d) = 150°

i.e., f + 3d = 150

The four angles are f, f + d, f + 2d, f + 3d.

f + f + d + f + 2d + f + 3d = 360°

f + f + d + f + 2d + 150 = 360°

3f + 3d = 360° - 150 = 210

3(f + d) = 210

f + d = \(\frac{210}{3}=70\)

The four angles are f, 70, f + 2d, 150 .

f + 2d = \(\frac{150+70}{2}=110\)

Common difference = 110 – 70 = 40

First angle = 70 – 40 = 30

So, the four angles are 30, 70, 110, 150

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