Question

In the diagram below AB⊥CD and bisects ∠MOP.(a) If m∠MOP=130° find m∠POD.(b) If m∠COM=38°, find m∠MOP and m∠POD.

Answer 1

A

Since AB in perpendicular to CD and bisects mThis can be written as

`m<\text{MOP}+m<\text{COM}+m<\text{DOP}=180\text{ (1)}`

but

`m<\text{COM}=m<\text{DOP}`

then

`m<\text{MOP}+2m<\text{DOP}=180`

pluggin the value of the angle m
`\begin{gathered} 130+2m<\text{DOP}=180 \\ 2m<\text{DOP}=180-130 \\ m<\text{DOP}=(50)/(2) \\ m<\text{DOP}=25 \end{gathered}`Therefore the angle m

B

As we mentioned above the angle mthen m

Using equation (1) of part to find the angle m
`\begin{gathered} m<\text{MOP}+38+38=180 \\ m<\text{MOP}=180-76 \\ m<\text{MOP}=104 \end{gathered}`therefore the angle m