Question

if two straight lines intersect each other and one pair of vertically opposite angles are complementary then the value of each angle of the other pair is​

Answer 1

Answer:

The two vertically opposite angles are complementary. That means their sum is 90⁰.

Then,

We know that Vertically opposite angles are equal. Hence, let it be x

so,

x + x = 90

→ 2x = 90

→ x = 45⁰

Now, let the other two V.O.A angles be y

45⁰ + 45⁰ + y + y = 360

→ 90⁰ + 2y = 360

→ 2y = 360 - 90

→ y = 270/2

→ y = 135

The value of each angle of other pair is 135⁰

Answer 2

Given:

Two straight lines intersect each other and one pair of vertically opposite angles are complementary

To find:

value of each angle of the other pair

Solution:

Angles are vertically opposite angles, so they are equal.

Let the value of one pair of vertically opposite angles be $x$ and the other pair be $y$.

The first pair of angles are also complementary angles, so the sum of the angles is 90°.

So,

$x+x=90$°

⇒$x=\frac{90}{2}$

⇒$x=45$°

Since the two straight lines are intersecting each other, then sum of all the angles will be 360°. So,

$y+y+x+x=360$°

⇒$2y+90$°$=360$°

⇒$2y=360$°$-90$°

⇒$2y=270$°

⇒$y=135$°

Hence, the value of each angle of the other pair is 135°.