Question

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

Answer 1

(a)

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

Answer 2

Option d. is correct

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