Question

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

Answer 1

Answer:

Option d. is correct

Step-by-step explanation:

Angle Sum Property :

Sum of angles of a triangle is $180^{\circ}$

In triangle ABD,

$38^{\circ}+56^{\circ}+x=180^{\circ}\\x+94^{\circ}=180^{\circ}\\x=180^{\circ}-94^{\circ}=86^{\circ}$

As x and z forms a linear pair, x + z = $180^{\circ}$

$86^{\circ}+z=180^{\circ}\\z=180^{\circ}-86^{\circ}=94^{\circ}$

In triangle ABC ,

$38^{\circ}+19^{\circ}+56^{\circ}+y=180^{\circ}\\113^{\circ}+y=180^{\circ}\\y=180^{\circ}-113^{\circ}=67^{\circ}$

So, option d. is correct

Answer 2

Answer:

(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