# Find the largest and smallest angles of a convex quadrilateral if they are proportional to the numbers 3: 7: 4: 6

March 28, 2021 | education

| Given:

АВСК – convex quadrilateral,

angle A: angle B: angle C: angle K = 3: 7: 4: 6,

Find the degree measures of the largest and smallest angles of a convex quadrilateral ABCK -?

Decision:

Consider a convex quadrilateral ABCK. It has the largest angle B and the smallest angle A.

Let one part be x degrees, then angle A is 3 * x degrees, angle B is 7 * x degrees, angle C is 4 * x degrees, angle K is 6 * x degrees. We know that the sum of the degree measures of a convex quadrilateral is 360 degrees. Let’s make the equation:

3 * x + 7 * x + 4 * x + 6 * x = 360;

x * 20 = 360;

x = 360: 20;

x = 18 degrees;

18 * 7 = 126 degrees – the largest angle B;

3 * 18 = 54 degrees – the smallest angle A.

Answer: 126 degrees; 54 degrees.

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