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### Geometry3.4 Problems on Quadrilaterals - III

 Example: The angles of a quadrilateral are x, x-10, x+30 and 2x. Find the angles. Solution: We know that the sum of the four angles of any quadrilateral is 360°. So, x + (x-10) + (x+30) + 2x = 360 x + x - 10 + x + 30 + 2x = 360 5x + 20 = 360 5x = 360 - 20 5x = 340 x = 340/5 x = 68° Substituting x value, we get 68°, 58°, 98° and 136°. Example: In a quadrilateral, the first angle is 7 more than the second, 3 less than the third and 5 times the fourth. Find the angles? Solution: Let the first angle be 'x'. Then the second angle will be 'x + 7'. The third angle and fourth angle will be 'x - 3' and '5x' respectively. Since the sum of the angles of a quadrilateral is 360°; we have x + x + 7 + x - 3 + 5x = 360; ie 8x + 4 = 360; ie 8x = 360 - 4 = 296; ie x = 296/8 = 37. Therefore first angle = 37°, second angle = 44°, third angle = 34° and fourth angle = 185°. Directions: Read the above example carefully and answer the following questions: In a quadrilateral, the first angle is 2 times the second, the remaining two angles are 5 more than the first. What is the measure of each of these angles? In a quadrilateral, the first angle is 6 times the second, 9 more than the third and 5 less than the fourth. What is the measure of each of these angles?
 Q 1: The angles of a quadrilateral are x, x+5, x+10 and 2x. Find the second and fourth angles.85°and 140° respectively.59° and 148° respectively.74° and 138° respectively.86° and 128° respectively. Q 2: The angles of a quadrilateral are x, x+20, x+30 and 2x. Find the first and fourth angles.62° and 124° respectively.70° and 140° respectively.74° and 148° respectively.69°and 138° respectively. Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!