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Two angles of an isosceles triangle measure 69 degrees and x degrees. What is the sum of all possible values of x?

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by vinodvinu

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by vinodvinu

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69 +2x =180

2x = 111

x = 55.5 degrees

If 69 and x are equal angles, x=69.

if x isthe third angle, x = 180-138 =42

Therefore sum is 69+55.5+42 = 166.5 degrres

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In an isosceles triangle there are two equal angles and a different angle. Let the triangle be ABC with angle A and B same and C different.

There are three possibilities:

Case-1:

A = 69

B = x = 69

C = 180 - (69+69) = 180-138 = 42

**So one possibility is x = 69**

Case-2:

A = 69

B = 69

C = x = 180 - (69+69) = 180-138 = 42

**So another possibility is x = 42**

Case-1:

C = 69

B = x

A = x

So x + x + 69 = 180

⇒ 2x = 180-69 = 111

⇒ x = 111/2 = 55.5

**So another possibility is x = 55.5**

**Sum of all possible values of x = 69+42+55.5 = 166.5**

There are three possibilities:

Case-1:

A = 69

B = x = 69

C = 180 - (69+69) = 180-138 = 42

Case-2:

A = 69

B = 69

C = x = 180 - (69+69) = 180-138 = 42

Case-1:

C = 69

B = x

A = x

So x + x + 69 = 180

⇒ 2x = 180-69 = 111

⇒ x = 111/2 = 55.5