The sum of the measures of three angles of a triangle is 180°. The middle-sized angle measures 1° more than 3 times the smallest angle. The middle-sized angle measures 101° less than the largest angle. Find the measure of the middle-sized angle.
2007-12-03 04:03:20 · 4 answers · asked by wrongnumber 1 in Science & Mathematics ➔ Mathematics
(3x +1) middle sized angle
+ x smallest angle
+ (3x+1)+101 largest angle 101 more than middle sized angle
= 180
simplify
7x + 103 = 180 solve for x
2007-12-03 04:17:18 · answer #1 · answered by realme 5 · 0⤊ 0⤋
Let the smallest angle be x, so the middle angle is 3x + 1, and the largest angle is 3x + 1 + 101 = 3x + 102, so:
x + 3x + 1 + 3x + 102 = 180, so
7x + 103 = 180, so
7x = 77, so
x = 11, and the 3 angles are:
11, 34, and 135 degrees.
Hope this helps, Twiggy.
2007-12-03 12:16:34 · answer #2 · answered by Twiggy 7 · 0⤊ 0⤋
Angles are A, B and C
B=A-101
C=(b-1)/3 or (A-102)/3
Thus
A+(A-101)+((A-102)/3)=180
Solve for A and then plug the number into the Equation for B.
Angles are 11, 34 and 135
2007-12-03 12:11:51 · answer #3 · answered by Marvinator 7 · 0⤊ 1⤋
let small angle = x
let middle angle be y
let largest angle be z
x + y + z = 180
3x - y = -1
y - z = -101
x =11, y = 34, z = 135
2007-12-03 12:16:57 · answer #4 · answered by Shyam S 2 · 0⤊ 0⤋