The measure of the angles of a triangle is 26° less than twice the measure of another angle. The measure of he third angle is 35°. Find the measure of the other two anges.
2007-09-20 18:49:38 · 6 answers · asked by rbrulesamanda 2 in Science & Mathematics ➔ Mathematics
the sum of the angles of a triangle is 180
so..........
180=(2x-26)+x+35
180=3x+35-26
180=3x+9
3x=180-9
x=57, your first angle
and your 2nd angle is
2x-26=2*57-26
2nd angle=88
2007-09-20 18:58:36 · answer #1 · answered by wiki_boy 2 · 1⤊ 1⤋
Angle A is 26 less than two times angle B.
A = 2B - 26
The measures of the three angles must total 180.
A + B + 35 = 180
Rewrite the two equations to have the variables on the left and the numbers on the right.
A - 2B = -26
A + B = 145 Subtract the first equation from this one.
3B = 171
B = 171/3 = 57 Substitute 57 for B in the second equation.
A + 57 = 145
A = 145 - 57 = 88
Check
88 + 57 + 35 = 180 It's right!
2007-09-20 19:01:59 · answer #2 · answered by ecolink 7 · 0⤊ 0⤋
The sum of the angles of a triangle is always 180. One angle is known (35) and one missing angle is twice and 26 less than the other unknown(lets call it x). Therefore, the sum of the angles can be represented as 35+x+(2x-26). Simply set this sum equal to 180 and solving for x gives you 57. So the angles in the triangle are 35, 57 and 88 (2(57)-26).
2007-09-20 19:04:01 · answer #3 · answered by Andrew S 2 · 0⤊ 1⤋
start with what u know ... a triangle has 180 degrees angle A is 35 degress ... so we subtract ... 180-35=145 ... the sum of angle B and C is 145 ... angle C = 2 times B - 26 ... then its easy ... if u have a hard time just guess and check ... example - you guess B =100 ... well u get 100 + (100 divided by 2 minus 26) 24 ... totals 124 ... to low so we go up ... 120 + (120 divided by 2 minus 26) 34 = 155 to high so u know its inbetween ... continue with the guess and check if needed
2007-09-20 20:13:32 · answer #4 · answered by Corey N 1 · 0⤊ 0⤋
Here are a couple hints to get you started.
The key is the fact that the three angles of a triangle add up to 180 degrees. So think to yourself: first + second + third = 180. Now look at the word problem and see what you know about the three angles.
One of them is going to be "x" and the other two will be written as expressions that might have an "x" in them, like "x-3" or "4x+1". Then you put those expressions into your sentence first + second + third = 180 and you have an equation, which you can solve to find x.
2007-09-20 19:11:20 · answer #5 · answered by dogwood_lock 5 · 0⤊ 1⤋
translate the english language statements to mathematical statements
let A,B,C represent the measure of each angle of the triangle
and recall that for any triangle A+B+C=180 (degrees)
so I assume your problem statement should begin with:
the measure of the angle (singular rather than plural!!!!)
of a triangle...
so we can write this as
A = 2B - 26 which can be rearranged as A-2B=-26
and
C = 35
now from the fact that A+B+C=180, we can substitute the
measure of C and get A+B+35=180 or A+B=145
now we have two equations in two unknowns (A&B) so solve them (there are several methods of doing so)
A+B=145
A-2B=-26
I'll subtract the second equation from the first to get:
3B = 171
B = 57
now from the first equation A = 145-B = 145-57= 88
so A=88 degrees and B=57 degrees
2007-09-20 19:06:38 · answer #6 · answered by Anonymous · 0⤊ 1⤋