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.
- The two triangles are similar when, x = 60°
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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