Answer:
x = 62°
Explanation:
You want the base angle in an isosceles triangle with a vertex angle of 56°.
Isosceles triangle
The sides of any triangle are proportional to the sine of the opposite angle. When two sides have the same measure, their opposite angles will have the same measure. Since the sum of angles in a triangle is always 180*, this means ...
56° +x° +x° = 180°
2x = 124° . . . . . . . . . . subtract 56°
x = 62° . . . . . . . . . . divide by 2
The measure of the angle marked x is 62°.
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Additional comment
The sides are all specified. This means you can find the angles of the triangle by solving it based on the side lengths. If you do that, you find that x ≈ 61.641°, as shown in the first attachment. This rounds to 62°.
As you can see in the second attachment, a better length for the side opposite the 56° angle would be 5.6 units instead of 5.7.
In short, the answer you get depends on how you use the given information.
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