A robot first follows the triangular test route $PQR$. The interior angles of the route are shown below.
By forming an equation in $t$, find $t$.
[2]

Question

A robot first follows the triangular test route $PQR$. The interior angles of the route are shown below.
By forming an equation in $t$, find $t$.
[2]
The robot then completes one circuit of a convex hexagonal route, turning left at every vertex. Each turning angle is measured from the forward extension of the side it has just travelled along.
1. Find the sum of the interior angles of this route.
  [1]
2. Three of the robot’s turning angles are each $50^\circ$. The other three are
  \[ (k+10)^\circ,\qquad (2k-5)^\circ,\qquad (k+25)^\circ. \]
  Find the smallest interior angle of the route. Show your working.
  [3]

Accepted Answer

(a) $t=20$. (b)(i) $720^\circ$. (b)(ii) $95^\circ$.

Polygons - Triangle Angle Sum and Exterior Angles