Question

In the given figure, l || m and n is a transversal. If angle c= 72 degree, find the measure of each of the angles a, b, d, e, f, g, h.​

please give full explanation

Answer 1

Answer:

a=g=f=72°

b=d=e=h=108°

Answer 2

★ Required Answer ★

Given:

• l || m and n is a transversal.

• $\rm { \angle c = 72° }$

To calculate:

• Measurement of each angle $\rm { a, b, d, e, f, g, h}$

Calculation:

We know that $\rm { \angle c = 72° }$, so

Measure of ∠ a :–

• $\rm \blue { \angle c = \angle a }$ [ Vertically opposite ]

$\rm { \implies \angle a = 72° }$

Measure of ∠ b :–

Since $\rm { \angle a }$ and $\rm { \angle b}$ forming linear pair, therefore,

• $\rm \blue { \angle b = 180° - \angle a}$ [ By linear pair ]

$\rm { \implies \angle b = 180° - 72° }$

$\rm { \implies \angle b = 108° }$

Measure of ∠ d :–

• $\rm \blue { \angle d = \angle b }$ [ Vertically opposite ]

$\rm { \implies \angle d = 108° }$

Measure or ∠ e :–

• $\rm \blue { \angle e = \angle d }$ [ Alternate Interior angles ]

$\rm { \implies \angle e = 108° }$

Measure of ∠ f :–

• $\rm \blue { \angle f = \angle c }$ [ Alternate Interior angles ]

$\rm { \implies \angle f = 72° }$

Measure of ∠ g :–

• $\rm \blue { \angle g = \angle f }$ [ Vertically opposite ]

$\rm { \implies \angle g = 72° }$

Measure of ∠ h :–

• $\rm \blue { \angle h = \angle e }$ [ Vertically opposite ]

$\rm { \implies \angle g = 108° }$

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