Question 15 Marks
In the given figure $\text{l || m}$ and t is a transversa. If $\angle1\ \text{and}\ \angle2$ are in the ratio 5 : 7 find the measure of each of the angles $\angle1,\ \angle2,\ \angle3\ \text{and}\ \angle8.$
Answer
Given: $\text{l || m}$ t is a transversal.$\angle1\ :\ \angle2\ =\ 5 : 7$
Let the angles measure 5x and 7x$\angle1+ \angle2=108^\circ$ (linear pair)
$\therefore\ 5\text{x}+7\text{x}=108^\circ$
$12\text{x}=180$
$ \text{x}=15$
$\therefore\ \angle1=5\text{x}=5(15)=75^\circ$
$\text{and}\ \angle2=7\text{x}=7(15)=105^\circ$
$\angle2+\angle3=180^\circ$ (linear pair)
$\angle3=180-105=75^\circ$
$\angle3+\angle6=180$ (interior angles on the same side of the transversal are supplementary)
$\angle6=180-\angle3=105^\circ$
and $\angle6=\angle8=105^\circ$ (vertically opposite angles)$\therefore\ \angle1=75^\circ$
$\angle2=105^\circ$
$\angle3=75^\circ$
$\angle8=105^\circ$
View full question & answer→ Given: $\text{l || m}$ t is a transversal.$\angle1\ :\ \angle2\ =\ 5 : 7$Let the angles measure 5x and 7x$\angle1+ \angle2=108^\circ$ (linear pair)
$\therefore\ 5\text{x}+7\text{x}=108^\circ$
$12\text{x}=180$
$ \text{x}=15$
$\therefore\ \angle1=5\text{x}=5(15)=75^\circ$
$\text{and}\ \angle2=7\text{x}=7(15)=105^\circ$
$\angle2+\angle3=180^\circ$ (linear pair)
$\angle3=180-105=75^\circ$
$\angle3+\angle6=180$ (interior angles on the same side of the transversal are supplementary)
$\angle6=180-\angle3=105^\circ$
and $\angle6=\angle8=105^\circ$ (vertically opposite angles)$\therefore\ \angle1=75^\circ$
$\angle2=105^\circ$
$\angle3=75^\circ$
$\angle8=105^\circ$
Given: AB || CD$\angle\text{ABE}=120^\circ$