Question

pls solve the answer in notebook...

Given l || m and angle 1 = 71° , find the measures of all other angles in the figure shown alongside.

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Answer 1

$\huge\bold{\mathtt{Question⇒}}$

Given $l\parallel m$ and $\angle1 = 71\degree$ , find the measures of all other angles in the figure shown alongside.

$\huge\bold{\mathtt{Given⇒}}$

• $l\parallel m$

• $\angle1 = 71\degree$

$\huge\bold{\mathtt{To\:find⇒}}$

The other angles.

$\huge\bold{\mathtt{Solution⇒}}$

We know that:

If two lines are parallel,

• Vertically opposite angles are equal.

• Corresponding angles are equal.

• Co-interior or allied angles are supplementary.

Here,

• $\angle1=\angle5$ (Corresponding angles)
• $\angle4=\angle8$ (Corresponding angles)
• $\angle2=\angle6$ (Corresponding angles)
• $\angle3=\angle7$ (Corresponding angles)

• $\angle1=\angle3$ (Vertically opposite angles)
• $\angle2=\angle4$ (Vertically opposite angles)
• $\angle5=\angle7$ (Vertically opposite angles)
• $\angle6=\angle8$ (Vertically opposite angles)

• $\angle1+\angle4=180\degree$ (Vertically opposite angles)

So,

$\angle1=\angle3=71\degree$

(Vertically opposite angles)

$\\ \angle3=\angle7=71\degree$

(Corresponding angles)

$\\ \angle7=\angle5=71\degree$

(Vertically opposite angles)

$\\ \angle1+\angle4=180\degree$

$\implies71\degree+\angle4=180\degree$

$\implies\angle4=180\degree-71\degree$

$\implies\angle4=109\degree$

So, $\angle4=109\degree$

$\\ \angle4=\angle2=109\degree$

(Corresponding angles)

$\\ \angle2=\angle6=109\degree$

(Vertically opposite angles)

$\\ \angle6=\angle8=109\degree$

(Vertically opposite angles)

$\huge\bold{\mathtt{Therefore⇒}}$

• $\angle1=71\degree$
• $\angle2=109\degree$
• $\angle3=71\degree$
• $\angle4=109\degree$
• $\angle5=71\degree$
• $\angle6=109\degree$
• $\angle7=71\degree$
• $\angle8=109\degree$

$\huge\bold{\mathtt{Done}}$

$\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

$\large\bold{\mathtt{Have\:a\:nice\:day.}}$