Question

Find the value of x

(25x)"
O x = 2
O x= 3
O x= 33
O x = 52
(45x)"
(57 + x)
R
S

Answer 1

x=3

Explanation:

Angles and Lines

We must recall:

• The sum of the internal angles of a triangle is 180°
• Two linear angles add up to 180°

The image shows a triangle and the extension of its base to form two linear angles.

Note from the triangle, angle R is what it takes to get to 180°:

`m\angle R=180-25x-(57+x)`

From the line SQ, angle R what it takes to get to 180°. Thus:

`m\angle R=180-45x`

Equating:

`180-25x-(57+x)=180-45x`

Subtracting 180 and simplifying:

`-25x-57-x=-45x`

`19x=57`

Dividing by 19:

x=3