Isosceles triangle's base angles 3y+4, 7x+5; other angle is

[Treeclimber]

The 2 base angles of the isosceles triangle are 3y+4 and 7x+5. The other angle is x+8y=1. How do I find the measure of each angle?

 

[stapel]

The 2 base angles of the isosceles triangle are 3y+4 and 7x+5. The other angle is x+8y=1.

Use what you know about the angle sum of any triangle, along with what you know about the relative sizes of the two base angles of any isosceles triangle. This knowledge allows you to create two equations (assuming the one "equals" sign is a typo for a "plus" sign):

. . . . .\(\displaystyle (3y\, +\, 4)\, +\, (7x\, +\, 5)\, +\, (x\, +\, 8y\, +\, 1)\, =\, 180\)

. . . . .\(\displaystyle 3y\, +\, 4\, =\, 7x\, +\, 5\)

The equations simplify somewhat as:

. . . . .\(\displaystyle 8x\, +\, 18y\, +\, 10\, =\, 180\)

. . . . .\(\displaystyle 3y\, =\, 7x\, +\, 1\)

Use any of the methods you've learned for solving systems of linear equations to find the values of x and y. For instance, you might proceed as follows:

. . . . .\(\displaystyle \left\{\begin{array}{=}4x\, +\, 9y\, =\, 85\\21x\, -\, 9y\, =\, -3\end{array}\right\}\)

Then add down, solve for x, back-solve for y, etc, etc.

Check my work! :wink:

 

[Treeclimber]

thank you so much but im still having trouble figuring it out
1st i misstyped the problem here it what it really looks like
2 base angles- 3y+4 and 7x+5 the other angle- x+8y=
1) first i added them all together- x+8y-1+3y+4+7x+5= 8x +11y+8=180 degrees
8x +11y+8=180 degrees
-8 -8
8x+11y= 172 degrees
2) 3y+4=7x+5
-4 -4
3y=7x +1
-7x -7x
3y-7x=1

3) i used the addition method
8x+11y=172
-7x+3y=1
I then multiplied 8x by 7 and -7x by 8
56x+77y=1376
-56x+24y=8
101y=1384
y=13.703
4) then i put y into 8x+11y=172
8x+11(13.703)=172
8x+150.733=172
-150.733 -150.733
8x=21.267
------------
8 8
x=2.658

5) I then tried to plug in the numbers to get the angles
3(13.703) +4=
41.109+4=
45.109

in the back of the book it says both base angles should be 40 so I know I've made a mistake i just don't know where

 

[mmm4444bot]

… The other angle is x+8y=1 …

… i misstyped the problem here it what it really looks like …

…the other angle- x+8y= … <<< This is still not a valid expression for an angle, and there is no need to type a minus sign after the word "angle".

From your subsequent statements, it appears that you're trying to type: x + 8y - 1.

Please pay more attention to what you post; use the preview button to proofread your posts before submitting them.

… i used the addition method … <<< This is not worded properly. You're using the "elimination" method.

… 56x+77y=1376 … <<< You made an arithmetic mistake. 7 times 172 is not 1376.

 

[Denis]

Even if quite messy, you made one mistake only:
56x+77y=1376
Should be =1204 : 172 * 7