Question

in the given triangle,find out x,y and z

Answer 1

ACB -
$180 - (60 + 50)$
x= 180-ACB(70)=110
EFG-
$180 - (70 + 60)$
z=180-EFG(50)=130
QRP-
$180 - (45 + 35)$
y=180-QRP(100 )=80
x=110;y=80;z=130

Answer 2

Concept:

We first recall the concept of geometry to solve this question

Geometry is that branch of mathematics that deals with the shapes,sizes, angles  and dimensions of things

To solve this question, we use the exterior angle theorem which states that:

"If a side of a triangle is produced , then the exterior  angle so formed is equal to the sum of the two interior opposite angles".

To find:

The angle x,y and z in the given figures

Solution:

In figure (1),

using exterior angle property,

     $x$ = $50^{0}+60^{0}$

so, $x =110^{0}$

In figure (2),

using exterior angle property,

     $z$ = $70^{0}+60^{0}$

so, $z =130^{0}$

In figure (3),

using exterior angle property,

     $y$ = $35^{0}+45^{0}$

so, $y =80^{0}$

Hence, the values are $x =110^{0}$,$y =80^{0}$ and $z =130^{0}$