Question

Determine all missing angles below.

Answer 1

Answer:

  a = 60, b = 19, c = 101, d = 79, e = 50

Step-by-step explanation:

Relations that are helpful here are ...

• vertical angles are congruent
• an exterior angle is equal to the sum of the opposite interior angles
• the sum of angles forming a straight angle is 180°
• the sum of angles in a triangle is 180°

__

Using these relations, we can find the unknown measures.

 a° = 60° . . . . . these are vertical angles

  51° +b° +110° = 180°   ⇒   b° = 180° -161° = 19° . . . . straight angle

  a° +b° +c° = 180°

  c° = 180° -60° -19° = 101° . . . . sum of angles in a triangle

  d° = 180° -101° = 79° . . . . . straight angle

 e° = c° -51° = 50° . . . . . c° is exterior to the triangle