Question

The measure of unknown angle x°, in the quadrilateral ABCD is .

• A. 115°
• B. 85°
• C. 105°
• D. 125°

Answer 1

The correct option is C 105°

Any quadrilateral can be divided into 2 triangles. So, the sum of the measures of internal angles of a quadrilateral is equal to the sum of the measures of internal angles of two triangles, i.e., 360°.



So, in quadrilateral ABCD, we can see :


$\angle ABC+\angle BCA+\angle CDA+\angle DAB=360°$

On substituting the respective values, we get:

$100°+75°+80°+x°=360°$

$\Rightarrow 255°+x°=360$

$\Rightarrow x°=360°-255°$

$\Rightarrow x°=105°$

So, value of x° is 105°.