Find the values of x, y, and z. The diagram is not to scale.

(a)

Step-by-step explanation:

using the following

The sum of the 3 angles in a triangle = 180°

The sum of the angles on a straight angle = 180°

To find x subtract the sum of the 2 given angles in the triangle from 180

x = 180 - (56 + 38) = 180 - 94 = 86 ( sum of angles in a triangle )

To find z, subtract x from 180

z = 180 - 86 = 94 ( angles on a straight angle )

To find y subtract the sum of the 2 angles from 180

y = 180 - (94 + 19) = 180 - 113 = 67

x = 86, y = 67 and z = 94

*check attachment for the correct figure given in this question with the right labelled angles

[tex]x = 86, y = 67, z = 94[/tex]

Step-by-step explanation:

From the given figure attached below, values of x, y, and z can be found as follow:

Value of x:

[tex]x = 180 - (38 + 56)[/tex] => sum of angles in a triangle

[tex]x = 180 - 94[/tex]

[tex]x = 86[/tex]

Value of z:

[tex]z = 180 - 86[/tex] => angles on a straight line

[tex]z = 94[/tex]

Value of y:

[tex]y = 180 - (19 + 94)[/tex] => sum of angles in a triangle.

[tex]y = 180 - 113[/tex]

[tex]y = 67[/tex]

[tex]x = 86, y = 67, z = 94[/tex]

Option d. is correct

Step-by-step explanation:

Angle Sum Property :

Sum of angles of a triangle is [tex]180^{\circ}[/tex]

In triangle ABD,

[tex]38^{\circ}+56^{\circ}+x=180^{\circ}\\x+94^{\circ}=180^{\circ}\\x=180^{\circ}-94^{\circ}=86^{\circ}[/tex]

As x and z forms a linear pair, x + z = [tex]180^{\circ}[/tex]

[tex]86^{\circ}+z=180^{\circ}\\z=180^{\circ}-86^{\circ}=94^{\circ}[/tex]

In triangle ABC ,

[tex]38^{\circ}+19^{\circ}+56^{\circ}+y=180^{\circ}\\113^{\circ}+y=180^{\circ}\\y=180^{\circ}-113^{\circ}=67^{\circ}[/tex]

So, option d. is correct

Option d. is correct

Step-by-step explanation:

Angle Sum Property :

Sum of angles of a triangle is [tex]180^{\circ}[/tex]

In triangle ABD,

[tex]38^{\circ}+56^{\circ}+x=180^{\circ}\\x+94^{\circ}=180^{\circ}\\x=180^{\circ}-94^{\circ}=86^{\circ}[/tex]

As x and z forms a linear pair, x + z = [tex]180^{\circ}[/tex]

[tex]86^{\circ}+z=180^{\circ}\\z=180^{\circ}-86^{\circ}=94^{\circ}[/tex]

In triangle ABC ,

[tex]38^{\circ}+19^{\circ}+56^{\circ}+y=180^{\circ}\\113^{\circ}+y=180^{\circ}\\y=180^{\circ}-113^{\circ}=67^{\circ}[/tex]

So, option d. is correct

Step-by-step explanation:

x = 81° because the sum of interior angles in a triangle is =180°

z = 99° because two interior angles = one exterior (or we can say x + z = 180°

y = 68° because y + z + 13 = 180°

The answer to your question is x= 81°, y= 68° and z = 99°

Step-by-step explanation:

Process

1.- Find the value of x°

The sum of the internal angles in a triangle equals 180°.

    36° + 63° + x° = 180°

    x° = 180° - 36° - 63°

    x° = 81°

2.- Find the value of z°

x° and z° are supplementary angles. The sum of supplementary angles measures 180°:

    x° + z° = 180°

   81° + z° = 180°

   z° = 180° - 81°

   z° = 99°

3.- Find the value of y°

The sum of internal angles measure 180°

   z° + y° + 13° = 180°

   99° + y° + 13° = 180°

   y° = 180° - 99° - 13°

   y ° = 68°

The value of x, y and z is 81°, 68° and 99° respectively.

Step-by-step explanation:

Consider the provided figure.

As we know the sum of all interior angles in a triangle is 180°.

Therefore,

36°+63°+x°=180°

99°+x°=180°

x°=180°-99°

x°=81°

Now find the value of z°

Angles on one side of a straight line is always equals to 180°.

Thus,

x°+z°=180°

81°+z°=180°

z°=180°-81°

z°=99°

Now find the value of y°

The sum of all interior angles in a triangle is 180°.

13°+z°+y°=180°

Substitute the value of z° in above equation.

13°+99°+y°=180°

112°+y°=180°

y°=180°-112°

y°=68°

Hence, the value of x, y and z is 81°, 68° and 99° respectively.

we know that

The sum of the internal angles in the triangle must be [tex]180[/tex] degrees

see the attached figure with letters to better understand the problem

Step [tex]1[/tex]

Find the measure of the angle x

In the triangle ABC

[tex]63\°+36\°+x\°=180\°[/tex]

solve for x

[tex]99\°+x\°=180\°[/tex]

[tex]x\°=180\°-99\°[/tex]

[tex]x=81\°[/tex]

therefore

the answer Part a)  is

the measure of angle x is [tex]81\°[/tex]

Step [tex]2[/tex]

Find the measure of the angle z

we know that

[tex]x+z=180\°[/tex] --------> by supplementary angles

substitute the value of x

[tex]81\°+z=180\°[/tex]

[tex]z=180\°-81\°[/tex]

[tex]z=99\°[/tex]

therefore

the answer Part b)  is

the measure of angle z is [tex]99\°[/tex]

Step [tex]3[/tex]

Find the measure of the angle y

In the triangle ACD

[tex]13\°+z\°+y\°=180\°[/tex]

solve for y

[tex]13\°+99\°+y\°=180\°[/tex]

[tex]112\°+y\°=180\°[/tex]

[tex]y\°=180\°-112\°[/tex]

[tex]y\°=68\°[/tex]

therefore

the answer Part c)  is

the measure of angle y is [tex]68\°[/tex]

x = 81°, z = 99°, y = 68°

Step-by-step explanation:

For a triangle, the sum of internal angles is 180°

So for the triangle in the left:

36 + 63 + x =180°

99 + x = 180

x = 180 - 99

x = 81°

For the triangle in the right:

x + z =180 since they are suplementary angles

81 + z = 180

z = 180 -81

z = 99°

an the sum of all the internal angles of the triangle in the right:

13 + 99 + y = 180

112 + y = 180

y = 180 - 112

y = 68°

x= 76, y = 63  z, 104

Step-by-step explanation:

We can find x since the three angles of a triangle add to 180 degrees

46+58+x = 180

104+x =180

Subtract 104 from each side

x = 180-104

x = 76

x and z form a straight line

x+z =180

76+ z = 180

Subtract 76 from each side

z = 180-76

z = 104

Z, 13 and y make a triangle

z+ 13 +y = 180

104+13+y = 180

117+y=180

Subtract 117 from each side

y = 180-117

y = 63