Answers:
10. b. [tex]\displaystyle 13[/tex]
9. b. [tex]\displaystyle 20[/tex]
8. a. [tex]\displaystyle 33[/tex]
7. a. [tex]\displaystyle 25°[/tex]
Step-by-step explanations:
10. Both segments are considered congruent, so turn both expressions into an equation:
[tex]\displaystyle 3x - 5 = x + 7 \hookrightarrow \frac{-12}{-2} = \frac{-2x}{-2} \\ \\ 6 = x[/tex]
Plug this back into the equation to get [tex]\displaystyle 13[/tex]on both sides.
9. All edges in a square obtain congruent right angles and edges, so set [tex]\displaystyle 45[/tex]equivalent to the given expression:
[tex]\displaystyle 45 = 2x + 5 \hookrightarrow \frac{40}{2} = \frac{2x}{2} \\ \\ \boxed{20 = x}[/tex]
8. Both angles are considered supplementary, so turn both expressions into an equation and set it to one hundred eighty degrees:
[tex]\displaystyle 180 = (4x - 15)° + (x + 30)° \hookrightarrow 180° = (15 + 5x)° \hookrightarrow \frac{165}{5} = \frac{5x}{5} \\ \\ \boxed{33 = x}[/tex]
7. In this rectangle, segment EO is a segment bisectour, making these angles Complementary Angles. Therefore, set an equation up to find its complement:
[tex]\displaystyle 90° = 65° + m\angle{VOE} \\ \\ \boxed{25° = m\angle{VOE}}[/tex]
I am joyous to assist you at any time.
