Question

If $X$ is a point on the line $AB$ and $Y,Z$ are points outside such that $\angle AXY={45}^o$ and $\angle YXZ={60}^o$, then $\angle AXZ$ is equal to

• A. ${120}^o$
• B. ${135}^o$
• C. ${150}^o$
• D. ${105}^o$

Answer 1

The correct option is D ${105}^o$

Given:$X$ is a point on line $AB;Y\&Z$ are outside points;

$\angle AXY={45}^{\circ }\&\angle YXZ={60}^{\circ }$

To Find:$\angle AXZ$

Solution:

Case1:$Y\&Z$ are on same side of $AB.$

$\therefore \angle AXZ=\angle AXY+\angle YXZ$

$\therefore \angle AXZ=45+60={105}^{\circ }$

Case2:$Y\&Z$ are on the opposite side of $AB.$

$\therefore \angle AXZ=\angle AXY+\angle YXZ=45+60={105}^{\circ }$

$\therefore \angle AXZ={105}^{\circ }$