Question

11. In the figure below, 2 || m, n llp and mz1 = 55°. Find the measure of each angle.22=23=23 47 8→n5 624 =26 =9 101112→P27 =28=M212 =210 =

Answer 1

Step 1

Given:

`\begin{gathered} m\angle1=55^o \\ l\mleft\Vert m\text{ and n}\mleft\Vert p\mright?\mright? \end{gathered}`

Step 2

Find the value of the missing angles with reason

`m\angle6=55^o\text{ (Vertically opposite angles are equal)}`
`m\angle2=\text{ 180 - m}\angle6=180-55=125^o(\text{ sum of angles on a straight line is 180 degrees)}`
`m\angle5=125^{o\text{ }}(vertically\text{ opposite angles are equal)}`
`m\angle9=m\angle1=55^o(\text{ corresponding angles are equal)}`
`m\angle10\text{ = 180 - m}\angle9=180-55=125^o(sum\text{ of angles on a straight line is 180 degre}es)`
`m\angle3=m\angle1=55^o(\text{corresponding angles are equal)}`
`m\angle4=m\angle2=125^o(corresponding\text{ angles are equal)}`
`m\angle7=m\angle5=125^o(corresponding\text{ angles are equal)}`
`m\angle11=m\angle9=55^o(correspondin\text{g angles are equal)}`
`m\angle8=m\angle6=55^o(corresponding\text{ angles are equal)}`
`^{}m\angle12=m\angle10=125^o(\text{ corresponding angles are equal)}`