# Find the largest and smallest angles of a convex quadrilateral if they are proportional

Find the largest and smallest angles of a convex quadrilateral if they are proportional to the numbers: a) 2: 4: 5: 7; b) 3: 7: 4: 6

a) Let one part be x degrees, then the first angle of the quadrilateral is 2 * x degrees, the second is 4 * x degrees, the third is 5 * x degrees, the fourth of the convex quadrilateral is 7 * x degrees. We know that the sum of the degree measures of the angles of a convex quadrilateral is 360 degrees. Let’s make the equation:
2 * x + 4 * x + 5 * x + 7 * x = 360;
18 * x = 360;
x = 360: 18;
x = 20 degrees;
2 * 20 = 40 degrees – the smallest angle of the quadrilateral;
20 * 7 = 140 degrees – the largest angle of the quadrangle;
b) Let one part be x degrees, then the first angle of the quadrilateral is 3 * x degrees, the second is 7 * x degrees, the third is 4 * x degrees, the fourth of the convex quadrilateral is 6 * x degrees. We know that the sum of the degree measures of the angles of a convex quadrilateral is 360 degrees. Let’s make the equation:
3 * x + 7 * x + 4 * x + 6 * x = 360;
20 * x = 360;
x = 360: 20;
x = 18 degrees;
3 * 18 = 54 degrees – the smallest angle of the quadrilateral;
18 * 7 = 126 degrees is the largest angle of the quadrangle.

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