Q4 of 35 Page 3

The angles of a quadrilateral are in the ratio 1:2:3:4. What are the measures of the four angles?

Given the ratio of the angles of a quadrilateral = 1:2:3:4
Therefore, let the angles of the quadrilateral be x, 2x, 3x and 4x.
The sum of the angles of a quadrilateral is 360°.
⇒ x+2x+3x+4x = 360°
⇒ 10x = 360°
⇒ x = 36°
⇒ 2x = 2 × 36° = 72°
⇒ 3x = 3 × 36° = 108°
⇒ 4x = 4 × 36° = 144°
∴ The measures of the four angles are 36°, 72°, 108° and 144°.

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2 In a quadrilateral ABCD, the measure of the three angles A, B and C of the quadrilateral are 110°, 70° and 80° respectively. Find the measure of the third angle. 3 In a quadrilateral ABCD, ∠ D is equal to 150° and ∠ A = ∠ B = ∠ C. Find ∠ A, ∠ B and ∠ C. 5 The In a quadrilateral
(i) which of them have their diagonals bisecting each other?
(ii) which of them have their diagonals perpendicular to each other?
(iii) which of them have equal diagonals ? 6 Adjacent sides of a rectangle are in the ratio 5: 12, if the perimeter of the rectangle is 34cm, find the length of the diagonal.