Use the given figure to solve for x
Answer (1)
[tex]\huge\color{skyblue}{Answer:}[/tex]22. [tex]m \angle TRI = 54\:[/tex] and [tex]\:m \angle DRI = 3[/tex] We are given that [tex]m\angle TRI = 54 [/tex] and [tex] m \angle DRI = 3x [/tex] Since these angles are on a straight line and adjacent, they add up to 180°.[tex]54 + 3x = 180[/tex][tex]3x = 180 - 54 = 12[/tex][tex]x = \frac{126}{3} = 42[/tex]So, [tex]\color{skyblue}{x = 42}[/tex]________________________23. [tex] m \angle URD = 2x + 8 [/tex] ,[tex] m \angle DRI = 3x + 14 \:[/tex] ,and [tex] \: m \angle URI = 7x - 2 [/tex] These three angles together form a full circle around point R, so they should add up to 360°.[tex](2x + 8) + (3x + 14) + (7x - 2) = 360 [/tex]Simplify the equation:[tex]2x + 3x + 7x + 8 + 14 - 2 = 360[/tex][tex]12x + 20 = 360[/tex][tex]12x = 360 - 20 = 340[/tex][tex]x = \frac{340}{12} = 28.33[/tex]So, [tex]\color{skyblue}{x = 28.33}[/tex]________________________24. [tex]m \angle URT = 12x - 5\: [/tex] and [tex] \:m \angle TRO = 3x + 45[/tex]Since these angles are adjacent and form a straight line, they add up to 180°.[tex](12x - 5) + (3x + 45) = 180[/tex]Simplify the equation:[tex]15x+40 = 180 [/tex][tex]15x =180-4 =140[/tex][tex]x = \frac{140}{15} \approx 9.33 [/tex] So, [tex]\color{skyblue}{x = \approx 9.33}[/tex]________________________25. [tex]m \angle ARU = 4x - 35 [/tex]and[tex] m \angle TRO = x + 10[/tex]Again, these angles form a straight line, so they sum to 180°.[tex](4x - 35) + (x + 10) = 180[/tex]Simplify the equation:[tex]5x - 25 = 180[/tex][tex]5x = 205[/tex][tex]x = \frac{205}{5} = 41[/tex]So, [tex]\color{skyblue}{x = 41}[/tex]________________________26. [tex] m \angle ARI = 9x + 18[/tex], [tex]m \angle ARD = 7x + 8[/tex], and [tex]\angle DRI = 4x - 10[/tex] The sum of these angles should be 180° since they form a straight line.[tex](9x + 18) + (7x + 8) + (4x - 10) = 180[/tex]Simplify the equation:[tex]20x + 16 = 180[/tex][tex]20x = 164 [/tex][tex]x = \frac{164}{20} = 8.2[/tex]So, [tex]\color{skyblue}{x = 8.2}[/tex]________________________ 27. [tex]m \angle URD = x + 6[/tex] ,[tex] m \angle DRI = 2x - 3[/tex], and [tex] m \angle URI = 45 [/tex]These angles should sum up to 360° since they form a full circle around R.[tex](x + 6) + (2x - 3) + 45 = 360[/tex]Simplify the equation:[tex]3x + 48 = 360[/tex][tex]3x = 312[/tex][tex]x = \frac{312}{3} = 104[/tex]So, [tex]\color{skyblue}{x = 104}[/tex]________________________28. [tex]m \angle ARU = \frac{1}{3}x + \frac{2}{3} [/tex] and [tex] m \angle URD = 2x + \frac{2}{3}[/tex]These angles form a straight line, so they sum to 80°.[tex] (\frac{1}{3} x + \frac{2}{3}) + (2x + \frac{2}{3} ) = 180[/tex]Simplify the equation:[tex]\frac{1}{3}x + 2x + \frac{4}{3} = 180[/tex]Combine like terms:[tex]\frac{1}{3}x + \frac{6}{3}x + \frac{4}{3} = 180[/tex][tex]\frac{7}{3}x + \frac{4}{3} = 180[/tex]Multiply the entire equation by 3 to eliminate the fractions:[tex]7x + 4 = 540[/tex][tex]7x = 536[/tex][tex]x = \frac{536}{7} \approx 76.57 [/tex]So,[tex]\color{skyblue}{ x \approx 76.57}[/tex]________________________[tex]\color{skyblue} {Learn\:more\:and\:work\:harder} [/tex]
