Question

In IJKL, side IJ || side KL ,∠I = 108° ∠K = 53° then find the measures of ∠J and ∠L. 
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Answer 1

☆Given Question?

In IJKL, side IJ || side KL ,∠I = 108° ∠K = 53° then find the measures of ∠J and ∠L. 

☆Required Answer:-

➭Value of ∠L is 72°.

➭Value of ∠J is 127°

☆Explaination:-

$\large \rm{ \underline {Given:-}}$

➭In IJKL, side IJ || side KL

➭∠I = 108° ∠K = 53°

$\large \rm{ \underline{To \: Find:- }}$

➭ Find the measures of ∠J and ∠L. 

$\large \rm{ \underline{Processing:- }}$

➭ See attachment for the diagram.

➭Side IJ || side KL and IL is their transversal.

✦We know that:-

∠I and ∠L = 180 (Interior angles property)

✦As per the Question,

$\implies \tt \angle I+ \angle L = 180^ {\circ}$

$\implies \tt 108^ {\circ}+ \angle L = 180^ {\circ}$

$\implies \tt \angle L = 180^ {\circ} - 108^ {\circ}$

$\implies \tt \angle L = 72^ {\circ}$

So, we got the value of ∠L i.e. 72°.

➭As per the formula given we will use it and will take out the value of ∠J.

∠J and ∠K= 180 (Interior angles property)

$\implies \tt \angle J+ \angle K = 180^ {\circ}$

$\implies \tt 53^ {\circ}+ \angle J = 180^ {\circ}$

$\implies \tt \angle J = 180^ {\circ} - 53^ {\circ}$

$\implies \tt \angle J = 127^ {\circ}$

So, we got the value of ∠J i.e. 127°.