Question

In the given figure, find the measure of each of the angles angleAOB , angleBOC , angleCOD and angleDOA
Who will answer fast I will mark them as a brainliest....​

Answer 1

★GIVEN★

• $\large{\sf{\angle\:AOB=x\degree}}$
• $\large{\sf{\angle\:BOC=2x\degree}}$
• $\large{\sf{\angle\:COD=3x\degree}}$
• $\large{\sf{\angle\:DOA=4x\degree}}$

★To Find★

• $\large{\sf{\angle\:AOB}}$
• $\large{\sf{\angle\:BOC}}$
• $\large{\sf{\angle\:COD}}$
• $\large{\sf{\angle\:DOA}}$

★SOLUTION ★

We know that sum of all angles is 360°.

According to the question,

$\large\implies{\sf{\angle\:AOB+\angle\:BOC+\angle\:COD+\angle\:DOA=360\degree}}$

$\large\implies{\sf{x+2x+3x+4x=360}}$

$\large\implies{\sf{10x=360}}$

$\large\implies{\sf{x=\dfrac{360}{10}}}$

$\large\implies{\sf{x=\dfrac{36\cancel{0}}{1\cancel{0}}}}$

$\large\therefore\boxed{\bf{x=36}}$

• $\large{\sf{x=36\degree}}$
• $\large{\sf{2x=2\times36=72\degree}}$
• $\large{\sf{3x=3\times36=108\degree}}$
• $\large{\sf{4x=4\times36=144\degree}}$

★VERIFICATION★

$\large\implies{\sf{\angle\:AOB+\angle\:BOC+\angle\:COD+\angle\:DOA=360\degree}}$

$\large\implies{\sf{36+72+108+144=360}}$

$\large\implies{\sf{360\degree=360\degree}}$

$\large\therefore\boxed{\bf{LHS=RHS}}$

Hence,

$\large{\red{\underline{\boxed{\therefore{\bf{1))\:\angle\:AOB=36\degree}}}}}}$

$\large{\red{\underline{\boxed{\therefore{\bf{2))\:\angle\:BOC=72\degree}}}}}}$

$\large{\red{\underline{\boxed{\therefore{\bf{3))\:\angle\:COD=108\degree}}}}}}$

$\large{\red{\underline{\boxed{\therefore{\bf{4))\:\angle\:DOA=144\degree}}}}}}$

Answer 2

$AOB=x°</p><p>\large{\sf{\angle\:BOC=2x\degree}}∠BOC=2x°</p><p>\large{\sf{\angle\:COD=3x\degree}}∠COD=3x°</p><p>\large{\sf{\angle\:DOA=4x\degree}}∠DOA=4x°</p><p>★To Find★</p><p>\large{\sf{\angle\:AOB}}∠AOB</p><p>\large{\sf{\angle\:BOC}}∠BOC</p><p>\large{\sf{\angle\:COD}}∠COD</p><p>\large{\sf{\angle\:DOA}}∠DOA</p><p>★SOLUTION ★</p><p>We know that sum of all angles is 360°.</p><p></p><p>According to the question,</p><p></p><p>\large\implies{\sf{\angle\:AOB+\angle\:BOC+\angle\:COD+\angle\:DOA=360\degree}}⟹∠AOB+∠BOC+∠COD+∠DOA=360°</p><p></p><p>\large\implies{\sf{x+2x+3x+4x=360}}⟹x+2x+3x+4x=360</p><p></p><p>\large\implies{\sf{10x=360}}⟹10x=360</p><p></p><p>\large\implies{\sf{x=\dfrac{360}{10}}}⟹x= </p><p>10</p><p>360</p><p> </p><p> </p><p></p><p>\large\implies{\sf{x=\dfrac{36\cancel{0}}{1\cancel{0}}}}⟹x= </p><p>1 </p><p>0</p><p> </p><p> </p><p>36 </p><p>0</p><p> </p><p> </p><p> </p><p> </p><p></p><p>\large\therefore\boxed{\bf{x=36}}∴ </p><p>x=36</p><p> </p><p> </p><p></p><p>\large{\sf{x=36\degree}}x=36°</p><p>\large{\sf{2x=2\times36=72\degree}}2x=2×36=72°</p><p>\large{\sf{3x=3\times36=108\degree}}3x=3×36=108°</p><p>\large{\sf{4x=4\times36=144\degree}}4x=4×36=144°</p><p>★VERIFICATION★</p><p>\large\implies{\sf{\angle\:AOB+\angle\:BOC+\angle\:COD+\angle\:DOA=360\degree}}⟹∠AOB+∠BOC+∠COD+∠DOA=360°</p><p></p><p>\large\implies{\sf{36+72+108+144=360}}⟹36+72+108+144=360</p><p></p><p>\large\implies{\sf{360\degree=360\degree}}⟹360°=360°</p><p></p><p>\large\therefore\boxed{\bf{LHS=RHS}}∴ </p><p>LHS=RHS</p><p> </p><p> </p><p>$