Find all possible values of x for which these two triangles are similar.

The two triangles are similar when two angles of the triangle are equal.

The possible value of x which the two triangles are similar is x = 60°

Reasons:

Required;

To find the values of x for which the two triangles are similar

Method:

Given that two angles of the triangle are specified, the triangles can be

similar for only one value of x.

Solution:

The two triangles are similar when we have;

x + 10° = 2·x - 50°

Which gives;

2·x - x = 50° + 10° = 60°

x = 60°

Checking gives;

x + 10° = 2·x - 50° = 70°

Two angles of the first triangle are;

70° and 60°

The third angle of the first triangle is (180° - (70° + 50°)) = 60°

The three angles of the first triangle are therefore; 70°, 60° and 50°.

Two angles of the second triangle are;

70° and 50°

The third angle of the second triangle is (180° - (70° + 50°)) = 60°

The three angles of the second triangle are therefore; 70°, 60° and 50°

Therefore, the two triangles are similar by AAA similarity.

When x = 50°, we have;

x + 10° gives;

50° + 10° = 60°

∴ ∠(x + 10°) = 60°

The two angles of the first triangle are; 60° and 50°

The third angle on the second triangle is 180° - (60° + 50°) = 70°

On the second triangle, we have;

2·x - 50° gives;

2 × 50° - 50° = 50°

∴∠(2·x - 50°) = 50°

Therefore, the two angles of the second triangle are; 50° and 50°

The third angle on the second triangle is 180° - (50° + 50°) = 80°

Therefore, the two triangles are not similar when x = 50°

Similarly, the two triangles are not similar when x + 10° = 50°

Therefore;

The possible value of x which the two triangles are similar is x = 60°

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I see no solution.

Step-by-step explanation:

The sum of the angles of a triangle is 180°

Given

x+ x + 10 +y = 180. and

2x -50 + 50 + y = 180

y represents the angles with no value indicated.

Simplifying:

2x +y +10 = 180

2x + y = 180

This looks like a no solution system.

If I'm missing something, I hope someone else can explain it.

so then what are you asking?

step-by-step explanation:

the answer is 1030 it's very simple math.