Question

Which equations are true for the values of x, y, and z? Select three options.

Answer 1

Answer:

Option A, B and C.

Step-by-step explanation:

It is given that 2 lines intersect to form 4 angles. Clockwise, from top, the angles are 65 degrees, x, y, z as shown below.

Sum of angles which lie on straight line is 180 degrees.

$x^{\circ}+65^{\circ}=180^{\circ}$         (linear pair)

If two lines intersect each other then vertically opposite angles are equal.

$x^{\circ}=z^{\circ}$                (Vertically opposite angle)

$y^{\circ}=65^{\circ}$                (Vertically opposite angle)

$x^{\circ}\neq 65^{\circ}$                (non-vertically opposite angle)

If two lines intersect each other then sum of 4 angles in 360 degrees.

$x^{\circ}+y^{\circ}+z^{\circ}+65^{\circ}=360^{\circ}$

$x^{\circ}+y^{\circ}+z^{\circ}=295^{\circ}$

Therefore, the correct options are A, B and C.

Answer 2

Answer:

A) x degrees + 65 degrees = 180 degrees

B) x degrees = z degrees

C) y degrees = 65 degrees

Step-by-step explanation:

Refer the attached figure

So,$\angle AOB = \angle COD (\text{Vertically opposite angles})$

$\angle AOB = 65^{\circ}$

$\angle COD = y$

So, $y=65^{\circ}$

$\angle AOB + \angle BOC = 180^{\circ} (\text{Linear pair})$

$\angle AOB = 65^{\circ}$

$\angle BOC = x$

So, $x+65^{\circ}=180^{\circ}$

$\angle BOC = \angle AOD (\text{Vertically opposite angles})$

So, x = z

So, Option A ,B and C are true for the values of x, y, and z