1)find the smallest square number which is divisible by 6,12 and 15
Break the numbers into their prime factorization:
6 = 2×3
12 = 2×2×3
15 = 3×5
A square number must have an even number of each prime factor.
So it must have two factors each of 2, 3, and 5. So the smallest
square number is 2×2×3×3×5×5 = 900
2)the opposite angles of a parallelogram are 2x+10 decree and 3x-20 degrees. Find all the angles of parallelogram.
The opposite angles of a parallelogram are equal. Set them equal and solve:
2x+10 = 3x-20
30 = x
So one pair of equal opposite angles are 30° each. The other pair of
opposite angles are supplementary to them, so they are 180°-30° or 150° each.
3)the 3 angles of a quadrilateral are in the ratio of 2:3:5 and the fourth angle is 60 decree. Find the measure of the first three angles.
Since the four angles of any quadrilateral have sum 360°, the three angles
in the ratio 2:3:5 have sum 360°-60° or 300°. Let their constant of
proportionality be k, then the three angles are 2k, 3k, and 5k
2k+3k+5k = 300°
10k = 300°
k = 30°
So the other three angles are
2k = 2(30°) = 60°
3k = 3(30°) = 90°
5k = 5(30°) = 150°
Edwin