Answer:
m<BGC = 145°
Step-by-step explanation:
<AGC and <DGB are vertical angles. Vertical angles are congruent. Therefore:
m<AGC = m<DGB
(substitution)
Collect like terms
Divide both sides by -5
x = 5
m<BGC = 180 - (m<AGC) (linear pair)
m<BGC = 180 - (3x + 20)
Plug in the value of x
m<BGC = 180 - (3(5) + 20) = 180 - 35
m<BGC = 145°
MO = 12 and PR = 3
Solution:
Given .
Perimeter of ΔMNO = 48
Perimeter of ΔPQR = 12
MO = 12x and PR = x + 2
<em>If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of perimeter of the triangles.</em>
Do cross multiplication.
Subtract 48x from both sides.
Divide by 96 on both sides, we get
⇒ 1 = x
⇒ x = 1
Substitute x = 1 in MO an PR.
MO = 12(1) = 12
PR = 1 + 2 = 3
Therefore MO = 12 and PR = 3.