Answer:
51°, 56°, 42° and 31°
Step-by-step explanation:
[tex](x - 5) + x + \frac{3}{4} x + \frac{1}{2} x + 3 = 180 \degree \\ (straight \: line \: \angle s) \\ \\ 2x + \frac{3}{4} x + \frac{1}{2} x + 3 - 5 = 180 \degree \\ \\ 2x + \frac{3}{4} x + \frac{2}{4} x - 2 = 180 \degree \\ \\ 2x + \frac{5}{4} x = 182 \degree \\ \\ \frac{2x \times 4 +5x }{4} = 182 \degree \\ \\ \frac{8x +5x }{4} = 182 \degree \\ \\ 13x = 182 \degree \times 4 \\ \\ x = \frac{182 \degree \times 4}{13} \\ \\ x = 14\degree \times 4 \\ \\ \huge \: \red{x = 56\degree} \\ \implies \\ \purple{ \boxed{ x - 5 = 56 - 5 = 51 \degree}} \\ \\ \frac{3}{4} x = \frac{3}{4} \times 56\degree \\ \\ \blue{ \frac{3}{4} x = 42\degree} \\ \\ \pink{ \frac{1}{2} x + 3 = 28 + 3 = 31 \degree}[/tex]
Thus, the measures of the given angles are: 51°, 56°, 42° and 31°
