Find x in a triangle with angles x and 65°.
Understand the Problem
The question is asking to find the value of angle x in a triangle where one angle is given as 65° and the other angle is marked as x. To solve this, we will apply the property that the sum of angles in a triangle is always 180°.
Answer
The angle \( x \) is \( 57.5^\circ \).
Answer for screen readers
The value of angle ( x ) is ( 57.5^\circ ).
Steps to Solve
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Use the Triangle Angle Sum Property The sum of the angles in a triangle is always 180°. We will use this property to find angle ( x ). Given angles are ( x ) and ( 65^\circ ).
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Set Up the Equation Set up the equation based on the triangle angle sum property: $$ x + 65^\circ + \text{(the third angle)} = 180^\circ $$
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Solve for the Third Angle Since there is no specific third angle given, we assume it must equal ( x ). Thus, we rewrite the equation as: $$ x + 65^\circ + x = 180^\circ $$
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Combine Like Terms Combine the like terms in the equation: $$ 2x + 65^\circ = 180^\circ $$
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Isolate the Variable Subtract ( 65^\circ ) from both sides to isolate the terms with ( x ): $$ 2x = 180^\circ - 65^\circ $$
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Calculate the Right Side Perform the subtraction: $$ 2x = 115^\circ $$
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Solve for ( x ) Now, divide both sides by 2 to solve for ( x ): $$ x = \frac{115^\circ}{2} = 57.5^\circ $$
The value of angle ( x ) is ( 57.5^\circ ).
More Information
In any triangle, the sum of all interior angles must equal ( 180^\circ ). The calculation ensures that the angles are consistent with the properties of triangles.
Tips
- Forgetting the Third Angle: Not considering that the sum of all angles must add up to ( 180^\circ ), including the third angle.
- Incorrectly Adding Angles: Make sure to combine angles carefully when setting up the equation.
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