Question

Fill in the missing angle measures. Given: ab and c d and <1 = 32°

Answer 1

hello

from the image given,

angle 1 = 32

`\begin{gathered} \angle1=\angle8 \\ \text{reaon: alternate angles are equal} \end{gathered}`
`\begin{gathered} \angle1=\angle3 \\ \text{reason:corresponding angles are equal} \\ \angle3=32^0 \end{gathered}`
`\begin{gathered} \angle1+\angle5=180^0 \\ \text{reason: angles on a straight line is equal to 180}^0 \\ \angle1=32 \\ 32+\angle5=180 \\ \angle5=180-32 \\ \angle5=148^0 \end{gathered}`
`\begin{gathered} \angle5+\angle6=180^0 \\ reason;\text{ angles on a straight line = 180} \\ \angle5=148 \\ 148+\angle6=180 \\ \angle6=180-148 \\ \angle6=32^0 \\ or\text{ we can simply say } \\ \angle1=\angle6 \\ \text{reason: opposite angles are equal} \end{gathered}`
`\begin{gathered} \angle5=\angle2 \\ \text{reason: opposite angles are equal} \\ \angle2=148^0 \\ or\text{ we can say }\angle1+\angle2=180\text{ since they are on a straight line} \end{gathered}`
`\begin{gathered} \angle3+\angle4=180^0 \\ \text{reason: angles on a straight line = 180} \\ 32+\angle4=180 \\ \angle4=180-32 \\ \angle4=148^0 \end{gathered}`
`\begin{gathered} \angle4=\angle7 \\ \text{reason: opposite angles are equal} \\ \angle7=148 \end{gathered}`
`\begin{gathered} \angle1=\angle8 \\ \text{reason; alternate angles are equal} \\ \angle8=38^0 \end{gathered}`

`\begin{gathered} \angle1=\angle14 \\ \text{alternate angles are equal} \\ \angle14=32^0 \end{gathered}`
`\begin{gathered} \angle5=\angle13 \\ \text{reason;corresponding angles are equal} \\ \angle13=148^0 \end{gathered}`
`\begin{gathered} \angle13=\angle10 \\ \text{reason:opposite angles are equal} \\ \angle10=148^0 \end{gathered}`
`\begin{gathered} \angle9=\angle14 \\ \text{reason:opposite angles are equal} \\ \angle9=32^0 \end{gathered}`
`\begin{gathered} \angle12=\angle13 \\ \text{reason: alternate angles are equal} \\ \angle12=148^0 \end{gathered}`
`\begin{gathered} \angle11+\angle12=180 \\ \text{reason:angles on a straight line equal 180}^0 \\ \angle11+148=180 \\ \angle11=180-148 \\ \angle11=32^0 \end{gathered}`
`\begin{gathered} \angle12=\angle15 \\ \text{reason : opposite angles are equal} \\ \angle15=148^0 \end{gathered}`
`\begin{gathered} \angle11=\angle16 \\ \text{reason: opposite angles are equal} \\ \angle16=32^0 \end{gathered}`

from the calculations above, it's evident we can use several ways to find angles in four parallel lines