Question

Ok, do not tell me "the picture isn't clear" it's clear, the question is just confusing which is why I am here, zoom in, by the way. There are two correct answers with everything being fully shown. Can you solve this simple question? Only 2 correct answers apparently. Last try

Answer 1

`\sf \angle PDT \cong \angle XF\:\!K`

`\sf m\angle PDT = m\angle XF\:\!K`

Explanation:

From inspection of the given diagram, we can see that ∠NAZ is congruent to ∠YBR, since they are both labelled 47°.

We use identical tick marks to indicate congruent angles. Therefore, as ∠NAZ and ∠MCS both have one tick mark, this means they are congruent. So the measure of ∠MCS is also 47°.

The remaining two angles, ∠PDT and
`\sf \angle XF\:\!K`, do not have a tick mark. This indicates that these angles are congruent (and different to the other three angles).

The symbol ≅ is used to show congruency. If we want to represent angle PDT is congruent to angle
`\sf XF\:\!K`, we write it as
`\sf \angle PDT \cong \angle XF\:\!K`.

This literally means "angle PDT is congruent to angle
`\sf XF\:\!K`".

If two angles are congruent, then their angle measures are equal.

When the angle measures are equal we write it as
`\sf m\angle PDT = m\angle XF\:\!K`.

The "m" means "measure", the "∠" means "angle", and "=" means "is equal to". So
`\sf m\angle PDT = m\angle XF\:\!K` means "the measure of angle PDT is equal to the measure of angle
`\sf XF\:\!K`".