Question

what are the values of t and u?
(figure of triangle pqr with q at top, p at bottom left, r at bottom right. sides qp and qr have a red mark each (indicating they are equal). angle at r is 72 degrees. angle at p is t degrees, angle at q is u degrees.)
t = \square^\circ
u = \square^\circ

Explanation:

Step1: Identify triangle type

The triangle has two equal sides ($QP=QR$), so it is isosceles with $\angle t = \angle R$.

Step2: Find value of $t$

$\angle R = 72^\circ$, so $t = 72^\circ$.

Step3: Calculate sum of known angles

Sum of $\angle t$ and $\angle R$: $72^\circ + 72^\circ = 144^\circ$.

Step4: Solve for $u$ using angle sum

Triangle angle sum is $180^\circ$, so $u = 180^\circ - 144^\circ$.

Answer:

$t = 72^\circ$
$u = 36^\circ$