Question

OT bisects ∠DOG. Find the measure of ∠DOG if ∠DOT = 4x + 4 and ∠TOG = 5x – 3

Answer 1

`\huge\boxed{64^o}`

Explanation:

If OT is bisects ∠DOG, then m∠DOT = m∠TOG. Therefore

`4x+4=5x-3` |subtract 4 from both sides

`4x+4-4=5x-3-4\\\\4x=5x-7`|subtract 5x from both sides

`4x-5x=5x-5x-7\\\\-x=-7`|change the signs

`x=7`

Calculate the measure of ∠DOG

m∠DOG = 2(m∠DOT)

`m\angle DOG=2(4\cdot7+4)=2(28+4)=2(32)=64`