208k views
20 votes
Determine all missing angles below.

Determine all missing angles below.-example-1
User MehulJoshi
by
3.6k points

1 Answer

5 votes

Answer:

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

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

User Ted Dziuba
by
3.3k points