Question

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answer 1

∠5 + ∠6 = 180°

∠2 + ∠3 = ∠6

∠2 + ∠3 + ∠5 = 180°

Explanation:

• ∠5 + ∠6 = 180° {Linear pair}
• ∠2 + ∠3 = ∠6 {Exterior angle property of triangle}
• ∠2 + ∠3 + ∠5 = 180° {Angle sum property of triangle}

Linear pair: If the non-common arms of two adjacent angles from a straight line, they are called linear pair. They add up to 180.

Exterior angle property of triangle: Exterior angle of a triangle is equal to the sum of opposite interior angles (remote angles).