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Solve for d in the given triangle, where the angles are 90°, 45°, and d°.

Mathematics

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Answer

45∘\text{45}^\circ

Step-by-step solution

4 steps
  1. Identify the type of triangle and its properties.

    The diagram shows a right-angled triangle, indicated by the square symbol, meaning one angle is 90∘90^\circ. The two short sides (legs) of the triangle are marked with single dashes, which means they are equal in length. This indicates that the triangle is an isosceles right-angled triangle.

  2. Determine the base angles of the isosceles triangle.

    In an isosceles triangle, the angles opposite the equal sides are also equal. Since the two legs are equal, the two acute angles must be equal. Let the unknown angle be dd. Therefore, the other acute angle is also dd.

  3. Apply the angle sum property of a triangle.

    The sum of the interior angles in any triangle is 180∘180^\circ.
    So, we can write the equation:

    90∘+d+d=180∘90^\circ + d + d = 180^\circ 90∘+2d=180∘90^\circ + 2d = 180^\circ
  4. Solve for dd.

    Subtract 90∘90^\circ from both sides:

    2d=180∘−90∘2d = 180^\circ - 90^\circ 2d=90∘2d = 90^\circ

    Divide by 2:

    d=90∘2d = \frac{90^\circ}{2} d=45∘d = 45^\circ

    Your calculation is correct. The value of dd is 45∘\boxed{\text{45}^\circ}.

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