Question

Same Side ExtellFor each diagram, find the measure of all the angles. Hi11. m Z1 = 95° m211 = 47°ad4N31316145876159b12Vo11с

Answer 1

11.

Consider that when a pair of parallel lines are intersected by a transversal, then,

1. the pair of alternate interior angles are equal.

2. the pair of corresponding angles are equal.

3. angles on the same side of transversal (co-interior angles) are supplementary.

Theorem: The sum of angles that constitute a straight line is always 180 degrees.

Theorem: When two lines intersect, the pair of vertically opposite angles are always equal.

Given that angle 1 measures 95 degrees,

`\angle1=95^(\circ)`

It implies that,

`\begin{gathered} \angle3=\angle1=95^(\circ)\text{ (vertically opposite angles)} \\ \angle1+\angle2=180^(\circ)\Rightarrow\angle2=85^(\circ)\text{ (straight line)} \\ \angle4=\angle2=85^(\circ)\text{ (vertically opposite angles)} \end{gathered}`

Thus, angles 2, 3, and 4 measure 85 degrees, 95 degrees, 85 degrees, respectively.

Also given that,

`\angle11=47^(\circ)`

It implies that,

`\begin{gathered} \angle9=\angle11=47^(\circ)\text{ (vertically opposite angles)} \\ \angle11+\angle10=180^(\circ)\Rightarrow\angle10=133^(\circ)\text{ (straight line)} \\ \angle12=\angle10=133^(\circ)\text{ (vertically opposite angles)} \end{gathered}`

Thus, angles 9, 10, and 12 measure 47 degrees, 133 degrees, 133 degrees, respectively.

Consider that there is no such information in the problem on the basis of which we can conclude the parallelity of lines.

So, the obtainable angles in the given figure are,

`\begin{gathered} \angle1=\angle3=95^(\circ) \\ \angle2=\angle4=85^(\circ) \\ \angle9=\angle11=47^(\circ) \\ \angle10=\angle12=133^(\circ) \end{gathered}`