what is the value of $p$?
(there is a triangle $uvt$ with $u$ at the top, $v$ at the bottom left, $t$ at the bottom right. the angle at $u$ is $36^circ$. the sides $uv$ and $ut$ have one red tick mark each, indicating they are equal in length.)

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# Explanation:
## Step1: Identify triangle type
The triangle $ UVT $ has two equal sides (marked with red ticks), so it's isosceles. Thus, $ \angle V = \angle T $ or $ \angle U $ is the vertex angle. Wait, no—wait, the equal sides are $ UV $ and $ UT $? Wait, no, the marks: one on $ UV $, one on $ UT $? Wait, no, looking at the diagram: the two sides with ticks are $ UV $ and $ UT $? Wait, no, actually, the sides $ UV $ and $ UT $ have ticks? Wait, no, the triangle has vertices $ U $, $ V $, $ T $. The sides with ticks: one on $ UV $, one on $ UT $? Wait, no, maybe $ UV = UT $? Wait, no, the base would be $ VT $, and the equal sides are $ UV $ and $ UT $. Wait, no, actually, the two sides with red marks are $ UV $ and $ UT $? Wait, no, maybe $ UV = UT $, so triangle $ UVT $ is isosceles with $ UV = UT $. Wait, no, the angle at $ U $ is $ 36^\circ $. Wait, no—wait, in an isosceles triangle, the angles opposite equal sides are equal. Wait, the two sides with ticks: let's see, the sides $ UV $ and $ UT $ have ticks? Wait, no, the diagram: $ U $ is the top, $ V $ and $ T $ are the base. The sides $ UV $ and $ UT $ have ticks? Wait, no, maybe $ UV = UT $, so angles at $ V $ and $ T $ are equal? Wait, no, wait, the angle at $ U $ is $ 36^\circ $. Wait, no, let's correct: the triangle has two sides equal: $ UV = UT $? Wait, no, the marks: one on $ UV $, one on $ UT $? Wait, no, maybe $ UV = VT $? Wait, no, the diagram shows two sides with red ticks: one on $ UV $, one on $ UT $. Wait, no, perhaps $ UV = UT $, so triangle $ UVT $ is isosceles with $ UV = UT $, so angles at $ V $ and $ T $ are equal. Wait, no, the angle at $ U $ is $ 36^\circ $. Wait, the sum of angles in a triangle is $ 180^\circ $. So if $ UV = UT $, then $ \angle V = \angle T $. Wait, no, wait, maybe the equal sides are $ UV $ and $ VT $? No, the ticks are on $ UV $ and $ UT $. Wait, let's re-express: in triangle $ UVT $, sides $ UV $ and $ UT $ are equal (marked by ticks), so it's isosceles with $ UV = UT $. Therefore, the base angles are $ \angle V $ and $ \angle T $, which are equal. Wait, no, wait: the angle at $ U $ is $ 36^\circ $, so the other two angles ($ \angle V $ and $ \angle T $) sum to $ 180 - 36 = 144^\circ $, and since they are equal (because $ UV = UT $), each is $ 144 / 2 = 72^\circ $. Wait, but the angle at $ V $ is $ p $. So $ p = 72^\circ $? Wait, no, wait—wait, maybe I got the equal sides wrong. Wait, the two sides with ticks: maybe $ UV = VT $? No, the ticks are on $ UV $ and $ UT $. Wait, let's check again. The triangle has vertices $ U $, $ V $, $ T $. The sides $ UV $ and $ UT $ have red ticks, so $ UV = UT $. Therefore, the angles opposite those sides: angle opposite $ UV $ is $ \angle T $, angle opposite $ UT $ is $ \angle V $. Wait, no: side $ UV $ is opposite angle $ T $, side $ UT $ is opposite angle $ V $. So if $ UV = UT $, then $ \angle T = \angle V $. The angle at $ U $ is $ 36^\circ $. So sum of angles: $ 36 + \angle V + \angle T = 180 $. Since $ \angle V = \angle T $, let $ \angle V = \angle T = x $. Then $ 36 + 2x = 180 $. Solve for $ x $: $ 2x = 180 - 36 = 144 $, so $ x = 72 $. Therefore, $ p = 72^\circ $.

## Step2: Calculate angle $ p $
Sum of angles in a triangle: $ 180^\circ $.
Given $ \angle U = 36^\circ $, and $ \triangle UVT $ is isosceles with $ UV = UT $, so $ \angle V = \angle T $.
Let $ \angle V = \angle T = p $.
Then:
$ 36^\circ + p + p = 180^\circ $
$ 36 + 2p = 180 $
Subtract $ 36 $ from both sides:
$ 2p = 180 - 36 = 144 $
Divide by $ 2 $:
$ p = \frac{144}{2} = 72^\circ $

# Answer:
$ 72^\circ $

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QUESTION IMAGE

Question

Explanation:

Step1: Identify triangle type

Step2: Calculate angle \( p \)

Answer: