Question

find angle \\(c\\) in this scalene triangle if \\(a = 75^{\circ}\\) and \\(b = 62^{\circ}\\).

Explanation:

⚡ Using what you learned: properties of triangles

Step 1: Use the Triangle Angle Sum Theorem

The sum of the interior angles in any triangle is always \( 180^\circ \):

$$ A + B + C = 180^\circ $$

Step 2: Substitute the known values and solve for C

Substitute \( A = 75^\circ \) and \( B = 62^\circ \) into the equation:

$$ 75^\circ + 62^\circ + C = 180^\circ $$

$$ 137^\circ + C = 180^\circ $$

$$ C = 180^\circ - 137^\circ $$

$$ C = 43^\circ $$

Answer:

43