Name: Parallel & Transversal Lines: Illustration
Uploaded: 2019-07-19
Duration: 6 min 20 s
Description: In geometry, the straight lines which do not meet are called parallel. A line that crosses a pair of parallel lines is known as transversal. Watch and learn...

Question

Write the values of the angles $a °$ to $h °$ and $k °$ , in the figure.

Accepted Answer

Given that the figure as follows.

Here we need to find values of the angles $a °$ to $h °$ and $k °$ .

Now from the figure,

$a ° + 150 ° = 180 °$ [Linear pairs of angles are supplementary]

i.e, $a ° = 180 ° - 150 ° = 30 °$

$a ° = 30 °$ .

Also,

$a ° + b ° = 180 °$ [Linear pairs of angles are supplementary]

$30 ° + b ° = 180 °$

$b ° = 180 ° - 30 ° = 150 °$

$b ° = 150 °$

Similarly,

$b ° + c ° = 180 °$ [Linear pairs of angles are supplementary]

i.e., $150 ° + c ° = 180 °$

$c ° = 180 ° - 150 ° = 30 °$

$c ° = 30 °$ .

Now from figure, the angles $a ° & d °$ are alternate angles and they are equal.

i.e., $a ° = d °$

i.e. $a ° = 30 ° = d °$

$d ° = 30 °$ .

Similarly we can see another pair alternate interior angles,

i.e., $f ° = 70 °$ [Pair of alternate angles interior are equal]

And

$f ° + g ° = 180 °$ [Linear pairs of angles are supplementary]

i.e., $70 ° + g ° = 180 °$

$g ° = 180 ° - 70 ° = 110 °$

$g ° = 110 °$ .

Also we have vertically opposite angles and they are equal.

i.e., $f ° = h °$

$f ° = 70 ° = h °$

$h ° = 70 °$ .

Similarly,

$g ° = k °$ [Vertically opposite angles and they are equal]

i.e., $g ° = 110 ° = k °$

$k ° = 110 °$ .

Again from figure, we can see a triangle with interior angles $a °, f °, & e °$ .

i.e., $a ° + f ° + e ° = 180 °$ [Sum of the interior angles in a triangle is $180 °$ ]

i.e., $30 ° + 70 ° + e ° = 180 °$

i.e., $100 ° + e ° = 180 °$

$e ° = 180 ° - 100 ° = 80 °$

$e ° = 80 °$ .

Write the values of the angles $a °$ to $h °$ and $k °$ , in the figure.

Important Questions on Parallel Lines

Learn and Prepare for any exam you want !

Write the values of the angles a° to h° and k°, in the figure.

Important Questions on Parallel Lines

Learn and Prepare for any exam you want !

Write the values of the angles $a °$ to $h °$ and $k °$ , in the figure.