Geometry Problem

Hint:

We know that P+Q+R=360 (exterior angles theorem) 

I don't understand how they add up to 360... Could you elaborate? Thanks.

Following up on CalTheGreat's tidbit on the exterior angle sum(the sum is important, as exterior angle theorem is something different) theorem, if you don't understand it, here's a proof:

Start by realizing that the interior angles of an n-gon have an angle sum of 180(n-2). This is derived from the fact that an n-gon can be divided into n-2 triangles, which all have an angle sum of 180 degrees(there are other derivations of it, but I think I'll use this one for now). Now if you look at an exterior angle, it's pair(the interior angle) forms a 180 degree angle, so the total sum of these pairs would be 180n(the exterior angles + the interior angles). Realize that because the interior angle sum is 180(n-2), the exterior angles sum is just:

\(180n-180(n-2) = 180n-180n+360 = 360\). That's just a short proof of why the exterior angles of a polygon ALWAYS add up to 360. 

The vertex that has the smallest experior angle is the one that has the largest interior angle.

So, you need to determine which angle, P, Q, or R must be the largest.

Then, to find the size of the exterior angle, subtract this value from 180°.

Assuming the P,Q and R are angles we have that

P   = Q + R             (1)

P + Q  +  R    = 180      (2)

Sub (1) into (2)  and we have that

P + P    = 180

2P  = 180

P    = 90

This will be the largest angle in the triangle......so.....it will have the smallest associated exterior angle.....and its associated exterior angle  will be supplemental    = 90°

Hi can someone help me with this problenm?

In triangle PQR, P= Q+R. Of all three exterior angles of triangle  what is the least exterior angle, in degrees?

Exterior angle theorem

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

Enterior angles:       ∠P = ∠Q + ∠R     ( ∠P  MUST be 90° )

∠P = 90°     ∠Q + ∠R = 90°

The sum of angles  Q and R is equal to the exterior angle at  P vertex.

The least exterior angle is at P vertex, and it's 90°.