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1.

2.

3.

4.

5.

Guest Nov 19, 2018
 #1
avatar+27229 
+1

1. This is an isosceles triangle, so 2x = 50º.  The sum of all the angles in a triangle must be 180º. These two bits of information are enough to allow you to calculate the value of y.

 

2. This is an isosceles triangle, with AB = AC. This allows you to find x and hence the size of BC.

 

3. Same as 2.

 

4.This is an equilateral triangle, so all the sides are the same length. Equate any two to find the value of x.

 

5. This is an equilateral triangle, so all the angles are equal to 60º.

Alan  Nov 19, 2018
 #2
avatar+92787 
+1

1.  Since AC   = BC.....the two base angles are equal  = 50°

 

And since the sum of three interior angles in a triangle  =  180°.......then

 

50 + 50 + 5y + 10   = 180

 

110 + 5y   =  180       subtract 110 from both sides

 

5y   =  70       divide both sides by 5

 

y  =  14

 

 

cool cool cool

CPhill  Nov 19, 2018
 #3
avatar+92787 
+1

2.    AC  =  AB    .....so

 

x + 8  =   2x  - 1           add 1 to both sides....subtract x from both sides

 

9  =   x

 

So....BC   =  3(9) - 3    =    24

 

 

cool cool cool

CPhill  Nov 19, 2018
 #4
avatar+92787 
+1

3.   Similar to 2

 

Because angle ACB  = angle ABC   then   AB   = AC

So

 

2x - 24   =  x - 2      add  24 to both sides, subtract x from each side    

 

x  =   22  =   BC  

 

 

cool cool cool

CPhill  Nov 19, 2018
 #5
avatar+92787 
+1

4 .

 

This is an equilateral triangle....so.....all sides are equal....so we can set any two sides equal and solve for x

 

4x - 10   = 3x + 2       add 10 to both sides.....subtract 3x from both sides

 

x  =   12

 

 

cool cool cool

CPhill  Nov 19, 2018
 #6
avatar+92787 
+1

5 .

 

An equilateral triangle has every interior angle  = 60°

 

So

 

7x - 3    =   60        add 3 to both sides

 

7x  = 63      divide both sides by 7

 

x   = 9    

 

 

 

cool cool cool

CPhill  Nov 19, 2018

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