Question

If x is a point on line AB and Y, Z are the points outside such that \[\angle AXY = {45^ \circ }\] and \[\angle YXZ = {60^ \circ }\] then \[\angle AXZ\] is equal to
A. \[{120^ \circ }\]
B. \[{135^ \circ }\]
C. \[{150^ \circ }\]
D. \[{105^ \circ }\]

Answer 1

Hint: x is a point on line AB and Y, Z are the points outside.We will solve this problem by drawing the diagram and getting the angles in consideration such that \[\angle AXZ\] is the sum of both the two angles given. So we can simply say that option D is the answer but we will write it in detail.

Step by step solution:
Given that, x is a point on line AB and Y, Z are the points outside. So we will draw this first.

This is the figure we will consider here. We have to find the angle coloured blue.
Now from figure we can clearly see that,
\[\angle AXZ = \angle AXY + \angle YXZ\]
Then just putting the values we get,
\[ \Rightarrow \angle AXZ = {45^ \circ } + {60^ \circ }\]
On adding the angles,
\[ \Rightarrow \angle AXZ = {105^ \circ }\]

Thus option D is the correct answer.

Note:
Note that the angle so formed here and the angle to be found are coincidently same thus it is easy to find. Also note that Y and Z are outside the line means they are not on the line AB like point x.
In case you were asked to find the angles related to point B we then need to make calculations like angles in linear pair and all. So be careful when you read the question!