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Sagot :

Answer with Step-by-step explanation:

1)

Given:

  • RA ≅ RM   (Legs of isosceles triangle are congruent.)
  • RA = x + 5
  • RM = 2x - 3
  • AM = x-3

Find the value of x:

2x - 3 = x + 5

2x - x = 5 + 3

x = 8

Find the length of each side of the isosceles triangle when x = 8:

RA = x + 5

RA = (8) + 5

RA = 13

RM = 2(8) - 3

RM = 16-3

RM = 13

MA = x - 3

MA = 8-3

MA = 5

2)

Given:  

  • RO is the base.
  • m∠R ≅ m∠O  (Base angles of isosceles triangle are congruent.)
  • m∠R = 4x-15
  • m∠O =2x + 25

Find the value of x:

4x - 15 = 2x + 25

4x - 2x = 25 + 15

2x = 40

2x/2 = 40/2

x = 20

Find the measures of base angles ∠R and ∠ O when x = 20:

m∠R = 4x-15

m∠R = 4(20) - 15

m∠R = 80 - 15

m∠R = 65°

m∠O =2x + 25

m∠O = 2(20) + 25

m∠O = 40 + 25

m∠O = 65°

Bonus:

The measure of vertex angle:

m∠P = 180 - 2(65)

m∠P = 180 - 130

m∠P = 50°