Question

Solve for z in the figure below.

Answer 1

z = 54

Explanation:

• x° = 45° (vertical angles)

• 5y° + 45° = 180° (Linear pair angles)

• -> 5y° = 180° - 45°

• -> 5y° = 135°

• -> y° = 135°/5

• -> y° = 27°

• Next, find the measures of the angles of the triangle.

• x° + 3y° + z° = 180° (By interior angle sum theorem of a triangle)

• -> 45° + 3(27°) + z° = 180°

• -> 45° + 81° + z° = 180°

• ->126° + z° = 180°

• -> z° = 180° - 126°

• -> z° = 54°

• -> z = 54