Question

Answer the following questions ​

Answer 1

Answer:

x = 65°

y = 110°

z = 120°

Step-by-step explanation:

BC = Angle 180°

115° + x = 180°

x = 65°

CD = Angle 180°

70° + y = 180°

y = 110°

AD = Angle 180°

60° + z = 180°

z = 120°

Answer 2

Answer

We shall find the values of the non given angles, accordingly as given in the question. First, we'll find the value of x. To find the values of all the variables, we use two concepts here. The first one is the 'straight line angle' property and the other is the 'angle sum property'.

First, we'll find the value of x.

Value of x :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {115}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \dashrightarrow \angle{x} = 180 - 115$

$\sf \dashrightarrow \angle{x} = {65}^{\circ}$

Now, let's find the value of y.

Value of y :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {70}^{\circ} + \angle{y} = {180}^{\circ}$

$\sf \dashrightarrow \angle{y} = 180 - 70$

$\sf \dashrightarrow \angle{y} = {110}^{\circ}$

Now, let's find the value of z.

Value of z :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {60}^{\circ} + \angle{z} = {180}^{\circ}$

$\sf \dashrightarrow \angle{x} = 180 - 60$

$\sf \dashrightarrow \angle{x} = {120}^{\circ}$

To find the value of w, first we should find the value of the other angle in the interior of the given figure.

Fourth interior angle :

$\sf \dashrightarrow {Angle \: sum \: property}_{(Quadrilateral)} = {360}^{\circ}$

$\sf \dashrightarrow {115}^{\circ} + {70}^{\circ} + {60}^{\circ} + \angle{B} = {360}^{\circ}$

$\sf \dashrightarrow {245}^{\circ} + \angle{B} = {360}^{\circ}$

$\sf \dashrightarrow \angle{B} = 360 - 245$

$\sf \dashrightarrow \angle{B} = {115}^{\circ}$

Now, let's find the value of w.

Value of w :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {115}^{\circ} + \angle{w} = {180}^{\circ}$

$\sf \dashrightarrow \angle{x} = 180 - 115$

$\sf \dashrightarrow \angle{x} = {65}^{\circ}$

Hence, the values of angles x, y, z and w are 65, 110, 120 and 65 degrees respectively.Thus, Option (A) is the correct option.