Question

Given A || B .

The value of x is _____ .

The measure of ∠1 is _____ °.

The measure of ∠2 is _____ °.

The measure of ∠3 is _____ °.

The measure of ∠4 is _____ °.

The measure of ∠5 is _____ °.

The measure of ∠6 is _____ °.

The measure of ∠7 is _____ °.

The measure of ∠8 is _____ °.

Angles 2 and 3 are _____ angles.

Answer 1

x=24, ∠1 = 101° , ∠2 = 79° , ∠3 = 101° , ∠4 = 101°, ∠5 = ∠6 = 79° , ∠7 = ∠8 = 89°.

Explanation:

We are given that, A || B.

It is known that 'the corresponding angles of parallel lines are equal and the opposite angles of the intersecting lines are equal.'

As, lines C and D are intersecting,

So, 3x+19 = 5x-29 i.e. 2x = 48 i.e. x=24.

Moreover, the sum of the four angles made by C and D is 360°.

Thus, (3x+19) + (5x-29) + 2∠7 = 360° i.e. 91+ 91 + 2∠7 = 360° i.e. 2∠7 = 360 - 182° i.e. 2∠7 = 178 i.e. ∠7 = 89°

Hence, ∠7 = ∠8 = 89°.

Again, lines B and D are intersecting,

As, x = 24. Then, in line B, we have, 4x+5 = 4×24+5 = 101.

So, we get, ∠4 = 101°

Moreover, the sum of the four angles made by B and D is 360°.

Thus, (4x+5) + 101 + 2∠5 = 360° i.e. 101+ 101+ 2∠5 = 360° i.e. 2∠5 = 360 - 202° i.e. 2∠5 = 158 i.e. ∠5 = 79°

Hence, ∠5 = ∠6 = 79°.

Since, A || B.

Then, ∠4 = ∠1, ∠6 = ∠2 and ∠3 = 4x+5=101°

Thus, ∠1 = 101° , ∠2 = 79° and ∠3 = 101°