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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.

In The Diagram Below ABCD And Bisects MOPa If MMOP130 Find MPODb If MCOM38 Find MMOP And MPOD class=

Sagot :

A

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

[tex]m<\text{MOP}+m<\text{COM}+m<\text{DOP}=180\text{ (1)}[/tex]

but

[tex]m<\text{COM}=m<\text{DOP}[/tex]

then

[tex]m<\text{MOP}+2m<\text{DOP}=180[/tex]

pluggin the value of the angle m[tex]\begin{gathered} 130+2m<\text{DOP}=180 \\ 2m<\text{DOP}=180-130 \\ m<\text{DOP}=\frac{50}{2} \\ m<\text{DOP}=25 \end{gathered}[/tex]Therefore the angle m

B

As we mentioned above the angle mthen m

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

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