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.)
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°
