How would I go about this Geometry problem (details below)?

Question

Triangle ABC is equilateral. Find the values of x, y, and z if angle A=19x+3, angle B=23y-3x, and angle C=5y+z. Show all work.

I'm not looking for you to do the problem for me, I just don't know what steps to take to solve the problem. Thanks.

Answer 1

if it is equilateral i, it is also equiangular so all angels equal 60 degrees...
so solve 19x + 3=60sub that in to ...23y-3x = 60 for x and solve for y and sub y into 5y + z = 60 and solve for z

Answer 2

In an equilateral triange, the three angles measure 60°.
For angle A:
19x + 3 = 60 --- Subtract 3 from both sides...
19x = 57 --- Divide both sides by 19...
x = 3

For angle B:
23y - 3x = 60 --- We know what x is...
23y - 3(3) = 60 --- Multiiply (-3)(3)...
23y - 9 = 60 --- Add 9 to both sides...
23y = 69 --- Divide both sides by 23...
y = 3

For angle C:
5y + z = 60 --- We know that y = 3...
5(3) + z = 60 --- Multiply (5)(3)...
15 + z = 60 --- Subtract 15 from both sides...
z = 45

Answer: x = 3; y = 3; and z = 45

Answer 3

EQUILATERAL!!!

All angles are equal to 60 degrees, since they must add up to 180.
Angle "A"- 60=19x+3
Angle "B"- 60=23y-3x
Angle "C"- 60=5y+z
Take two and try to eliminate a variable. "A" and "B" end up with: y=3. Substitute that into: 60=23y-3x
60=23(3)-3x
60=69-3x
-9=-3x
3=x

Sub. the Y into 60=5y+z
60=5(3)+z
60=15+z
45=z
x=3
y=3
z=45

Answer 4

Since it is an equilateral triangle, you know all angles are 60 degrees. A=60, B=60, and C=60. Just solve for x and y.

You can find X easily. 60=19x+3 therefore, 19x=57, therefore x=3

Substitue 3 for x in the rest of the equations.

Answer 5

A = B = C = 60°

So 19x + 3 = 60 → x = 3
23y - 3x = 60 → y = 3
5y + z = 60 → z = 45

Answer 6

If ABC is equilateral, then it's also equiangular.

So

19x + 3 = 23y - 3x
19x + 3 = 5y + z
23y -3x = 5y + z

3 equations in 3 unknowns. Hopefully solvable. Good luck. :)

Answer 7

since it is an equillateral, the all 3 angles are congruent to each other and one interior angle is 60
19x+3=60
23y-3x=60
5y+z=60

first equation
x=3

sub 3 for x in the second equation.
23y-3(3)=60
23y-6=60
23y=66
y=66/23

sub 66/23 for y in the third equation.
5(66/23)+z=60
z=1050/23

Answer 8

well, if you remember back to algebra one, you'll have to do some equation solving. add up (19x+3)+(23y-3x)+(5y+z) combining like terms. then set that all equal to 180 (because its a triangle and solve the equation.


that is, solve (16x+28x+z+3=180)

Answer 9

equilateral means all angles are same, right?

so A=B=C=60 degrees.

you get x from A equation, then use that to get y out of B, and then find z from C.

Answer 10

Hi dbn, Internal angle of a regular polygon is given by (n-2)*180 / n In your case, it is 80 degrees. Therefore (n-2)*180 / n = 80 or 180n-360 = 80n or n = 3.6 which is NOT logical. Pls submit your question again.