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Find x° = ?

Mathematics

ScanSolve AI Answer

Answer

130

Step-by-step solution

2 steps
  1. Identify the interior angle at the top vertex of the triangle.

    The angle 95∘95^\circ is an exterior angle to the triangle at the top vertex. An interior angle and its adjacent exterior angle form a linear pair, meaning their sum is 180∘180^\circ.
    Let the interior angle at the top vertex be α\alpha.

    α=180∘−95∘\alpha = 180^\circ - 95^\circ α=85∘\alpha = 85^\circ
  2. Apply the exterior angle theorem.

    The exterior angle of a triangle is equal to the sum of its two opposite interior angles. In this case, x∘x^\circ is the exterior angle, and the two opposite interior angles are 45∘45^\circ and α\alpha.

    x∘=45∘+αx^\circ = 45^\circ + \alpha

    Substitute the value of α\alpha from Step 1:

    x∘=45∘+85∘x^\circ = 45^\circ + 85^\circ x∘=130∘x^\circ = 130^\circ

    The value of xx is:

    130130
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