Library / CEMC Pascal /226 of 603

CEMC Pascal, 2020

Geometry Difficulty 1.3 Junior Find the answer Canada

In the diagram, three lines intersect at a point.

What is the value of $x$ ?

$30$
$45$
$60$
$90$
$120$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since opposite angles are equal, then the three unmarked angles around the central point each has measure $x^\circ$ .

Since the angles around a point add to $360^\circ$ , then $6 \times x^\circ = 360^\circ$ .

From this, $6x = 360$ and so $x = 60$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.