ANSWERS:
Activity 2. Challenge Yourself!
For Number One.
[tex] \large\begin{array}{l}\tt \overline{ST} \cong \overline{AX}\\\tt 16-2x=5x+9\\ \tt 16 - 9 = 5x + 2x \\ \tt 7 = 7x \\ \tt x = 7 \div 7 =\boxed{\tt1}\end{array}[/tex]
For Number Two.
[tex]\large\begin{array}{l}\tt \angle LAK \cong \angle UAS\\\tt \frac{5}{4} x + \frac{1}{2} =2x - \frac{1}{2} \\ \tt \frac{5}{4} x - 2x = - \frac{1}{2} - \frac{1}{2} \\ \tt \frac{5 - 8}{4} x = - \frac{2}{2} \\ \tt - \frac{3}{4} x = - 1 \\ \tt x = - 1 \div - \frac{3}{4} \\ \tt x = 1 \times \frac{4}{3} = \boxed{ \tt\frac{ 4}{3} } \end{array}[/tex]
For Number Three.
[tex]\large\begin{array}{l}\tt \angle SLI \cong \angle ALV\\\tt 23 \degree = ( \frac{x}{3} + 26) \degree \\ \tt 23 \degree - 26 \degree = \frac{x}{3} \degree \\ \tt - 3 \degree = \frac{x}{3} \degree \\ \tt x = (- 3)(3) \\ \tt x = \boxed{\tt- 9}\end{array}[/tex]
For Number Four.
[tex]\large\begin{array}{l}\tt \overline{ZA} \cong \overline {AR}\\\tt \frac{1}{2} x - 3 = 2 - \frac{3}{4} x \\ \tt \frac{1}{2} x + \frac{3}{4} x = 2 + 3 \\ \tt \frac{2 + 3}{4} x = 5 \\ \tt \frac{5}{4} x = 5 \\ \tt x = 5 \div \frac{5}{4} \\ \tt x = 5 \times \frac{4}{5} \\ \tt x = \boxed{\tt4 }\end{array}[/tex]
