1, The smallest angle of a trianlge is 70 degree. Find the other two angles if we know that they differ
by 6 degree:
2. The sum of the inner angles of a polygon is 5580 degree. How many sides does the polygon have?
2007-01-28 14:01:51 · 8 answers · asked by do you smell..... what's coo 4 in Science & Mathematics ➔ Mathematics
1) The smallest angle of a trianlge is 70 degree. Find the other two angles if we know that they differ
by 6 degree:
The angles of a triangle always add up to 180°.
70 + x + (x + 6) = 180
2x + 6 = 110
2x = 104
x = 52
x + 6 = 58
The angles of the triangle are 52°, 58°, and 70°.
2. The sum of the inner angles of a polygon is 5580 degree. How many sides does the polygon have?
The measure of one interior angle for a regular polygon with n sides is 180(1 - 2/n). The measure for all of them is 180(n - 2). So we have the equation:
180(n - 2) = 5580
n - 2 = 5580/180 = 31
n = 31 + 2 = 33
The polygon has 33 sides.
2007-01-28 14:47:26 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋
1. The other two angles add up to 110° and differ by 6°, so we have x + y = 110 and x - y = 6. Solving gives 58° and 52° as the answer. Note that the given angle is in fact the largest angle of the triangle! It is impossible for any triangle to have a smallest angle of more than 60°.
2. If the polygon has n sides, we can divide it into n triangles each with one side as the base and vertex at the centre of the polygon. The sum of all their angles is n*180°, of which 360° are in the centre. So the sum of the interior angles of the polygon is (n-2)*180°. Setting this equal to 5580 gives n - 2 = 5580/180 = 31, so the polygon has 33 sides.
2007-01-28 22:13:08 · answer #2 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
1. Let x be the largest of the two angles:
70 + (x) + (x-6) = 180 - solve for x (which is x=58)
Therefore the two other angles are 58 and 52. Check 70+58+52 = 180. Note that 70 is not the smallest angle, but the largest.
2. Inner angle sum of a polygon with n sides is (n-2) x 180. So you take (n-2)x180=5580 (which is n=33)
2007-01-28 22:16:17 · answer #3 · answered by Ivan 5 · 0⤊ 0⤋
1. Well, first u do 180-70, which equals 110, then divide by 2, giving u 55, then just add or take 3 from 55 to give u the answers, which would be 52 and 58.
2. Well the formula to find the sum of the interior angles is 180(n-2), n= number of angles. So
5580=180(n-2)
5580/180=n-2
31=n-2
n=33
2007-01-28 22:12:14 · answer #4 · answered by socbaskmth 2 · 0⤊ 0⤋
For triangle, sum of angle = 180 degree
If we know one of angle = 70 degree while the other two difer by 6 degree, then
70 + A + (A +6) = 180
2A = 104
A = 52 degree
So, the triangle has angle 70 degree, 52 degree and 58 degree.
The 70 degree is largest angle, not smallest one.
The inner angle for poligon is as below
n (180 - 360/n) = 5580
180n - 360 = 5580
180 n = 5940
n = 33 sides
2007-01-28 22:18:02 · answer #5 · answered by seah 7 · 0⤊ 0⤋
1) n + n + 6 + 70 = 180, and solve.
All three angles must have a sum of 180 in a triangle.
2. (n-2)180 = 5580, and solve
n refers to the number of sides.
2007-01-28 22:11:30 · answer #6 · answered by mirramai 3 · 0⤊ 0⤋
the sum of all angles is 180 degrees right? so you need two numbers that match up to 110 and are 6 apart. can't get any simpler than that without giving you the answer. It's your homework assignment.
2007-01-28 22:10:32 · answer #7 · answered by swksmason 3 · 0⤊ 0⤋
1. 180 (degrees in triangle) - 70 =110
110 divided by 2 (the other angles) = 55
55 + 6 (this will be the bigger remaining angle) = 61
55 - 6 (this will be the smaller of the remaining) = 49
as for 2. it's too complex for my little twelve year old mind
PS: you spelled triangle rong
2007-01-28 22:26:47 · answer #8 · answered by Chimpanzees? Monkey. 7 · 0⤊ 0⤋