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| 1. |
ABCD is a cyclic quadrilateral .find tha sngle if tha cyclic quadrilatrtal. |
| Answer» We know that the sum of the measures of opposite angles in a cyclic quadrilateral is 180°.{tex}\\therefore{/tex}{tex}\\angle{/tex}A + {tex}\\angle{/tex}C = 180°{tex}\\Rightarrow{/tex} 4y + 20 - 4x = 180°{tex}\\Rightarrow{/tex} -4x + 4y = 160°{tex}\\Rightarrow{/tex} x - y = -40° ....(1)\xa0Also {tex}\\angle{/tex}B + {tex}\\angle{/tex}D = 180°{tex}\\Rightarrow{/tex} 3y - 5 - 7x + 5 = 180°{tex}\\Rightarrow{/tex} -7x + 3y = 180°............... (2)Multiplying equation (1) by 3, we obtain:3x - 3y = -120° ..... (3)Adding equations (2) and (3), we obtain:-4x = 60°{tex}\\Rightarrow{/tex} x = -15°Substituting the value of x in equation (1), we obtain:-15 - y = 40°{tex}\\Rightarrow{/tex} y = -15 + 40 = 25°{tex}\\therefore{/tex}{tex}\\angle{/tex}A = 4y + 20 = 4 {tex}\\times{/tex}\xa025 + 20 = 120°{tex}\\angle{/tex}B = 3y - 5 = 3 {tex}\\times{/tex}\xa025 - 5 = 70°{tex}\\angle{/tex}C = -4x = -4 {tex}\\times{/tex}\xa0(-15) = 60°{tex}\\angle{/tex}D = -7x + 5 = -7(-15) + 5 = 110° | |