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Solve for x in the given geometric diagram, where angles are marked as 75°, 65°, 70°, and x°.

Mathematics

ScanSolve AI Answer

Answer

55∘55^\circ

Step-by-step solution

4 steps

  1. The sum of the interior angles in any triangle is 180∘180^\circ.

    60∘+65∘+x∘=180∘60^\circ + 65^\circ + x^\circ = 180^\circ

  2. Add the known angles.

    65∘=60∘+5∘65^\circ = 60^\circ + 5^\circ 60∘+65∘=125∘60^\circ + 65^\circ = 125^\circ

  3. Substitute the sum into the equation.

    125∘+x∘=180∘125^\circ + x^\circ = 180^\circ

  4. Subtract 125∘125^\circ from both sides.

    x∘=180∘−125∘x^\circ = 180^\circ - 125^\circ x∘=55∘x^\circ = 55^\circ

    Final answer: 55∘\boxed{55^\circ}

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