# Find all the angles of the convex quadrilateral AKMB, if it is known that the angles A and K are equal

Find all the angles of the convex quadrilateral AKMB, if it is known that the angles A and K are equal, the angle M is six times less than the angle A, and 3/5 of the angle B is 60 degrees.

1. Having made the proportion, we calculate the degree measure ∠В:

3/5 – 60 °;

1 – x °;

x = 60: 3/5 = 60 x 5/3 = 100 °.

∠В = 100 °.

2. We take the value of ∠A for x. The value of ∠К is also x, since, according to the condition of the problem, these angles are equal. ∠M – x / 6.

3. Considering that the sum of all internal angles of a convex quadrilateral is 360 °, we compose the equation:

x + x + x / 6 + 100 = 360;

(6x + 6x + x) 6 = 260;

13x = 6 x 260;

x = 120 °.

∠А = ∠К = 120 °.

∠M – 120/6 = 20 °.

Answer: the angles of a given convex quadrilateral ∠B = 100 °, ∠A = ∠K = 120 °, ∠M = 20 °.

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