✒️SQUARE
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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]
[tex] \qquad \LARGE \:\: \rm m\angle USR = 45\degree [/tex]
*Please read and understand my solution. Don't just rely on my direct answer*
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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]
The diagonal of the square bisects the its angle. Therefore:
- [tex] \rm m\angle USR = m\angle UST [/tex]
Let us consider that angle RST is a right angle. Thus, angles USR and UST are complementary.
- [tex] \rm m\angle USR + m\angle UST = m\angle RST [/tex]
- [tex] \rm m\angle USR + m\angle UST = 90\degree [/tex]
Substitute the measure of angle UST as the measure of angle USR.
- [tex] \rm m\angle USR + m\angle USR = 90\degree [/tex]
- [tex] \rm 2(m\angle USR) = 90\degree [/tex]
- [tex] \rm \frac{2(m\angle USR)}2= \frac{\,90\degree}2 \\ [/tex]
- [tex] \rm m\angle USR = 45\degree [/tex]
Therefore, the measure of angle USR is 45°
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(ノ^_^)ノ [tex] \large\qquad\qquad\qquad\tt 3/1 /2022 [/tex]
