A geometry problem by Hana Wehbi

Geometry Level 3

In the diagram, if $\triangle ABC$ and $\triangle PQR$ are equilateral, then find the measure of $\angle CXY$ in degrees.

25 40 35 50 30

2 solutions

. .
Feb 25, 2021

I used a protractor. And I got $\angle CXY = 40 \degree$ .

But the problem still requires a logical solution, some figures may not be drawn to scale so a method would be handy in these situations.

Hana Wehbi - 3 months, 2 weeks ago

Marta Reece
Mar 19, 2017

The three angles above the horizontal line at $P$ have to add up to $180^\circ$ , so $\angle BPY=180-60-75=45^\circ.$

The same has to be true at point $B$ , giving us $\angle PBY=180-60-65=55^\circ$ .

Angles in the triangle $PBY$ have to add up to $180^\circ$ , to $\angle BYP=180-45-55=80^\circ$ .

$\angle CYX=\angle BYP=80^\circ$ .

Angles in the triangle $XYC$ have to add up to $180^\circ$ , to $\angle YXC=180-80-60=40^\circ$ .

Nice solution. Thank you for posting it.

Hana Wehbi - 4 years, 2 months ago