Answer and Step-by-step explanation:
Because of the vertical angles theorem, the angle that is 65 degrees would be equal to y.
y = 65°
X and Y are supplementary angles, which form a linear lair. This linear pair will add up to 180 degrees.
TO find x, we subtract 65 from 180.
180 - 65 = 115
x = 115°
X and Z are vertical angles, so they are equal to each other.
z = 115°
x = 115°
y = 65
z = 115°
To solve for the length of PQ, we would use the Pythagorean theorem equation.
[tex]a^{2} +b^{2}= c^{2} \\\\\\a = PQ\\\\b = QR\\\\c = PR\\\\\\a^{2} + 24^{2} = 25^{2} \\\\a^{2} + 576 = 625\\\\a^{2} = 49\\\\a = 7[/tex]
The length of PQ is 7.
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