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In a parallelogram ABCD find the measure of all the angles if one of its angle is 15° less than twice the smallest angle |
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Answer» please mark as brainliest answer hope this helps you! Step-by-step explanation: All the angles are 65°, 115°, 65°, 115°. Step-by-step explanation: Let the smallest angle be 'x'. So, the other angle is 15 degrees less than twice the smallest angle. Mathematically, it is EXPRESSED as 2x-152x−15 since we know that in case of PARALLELOGRAM, opposite angles are equal. so, four angles must be x,x , 2x-15, 2x-15 We know that sum of all angles in quadrilateral is 360°. So, it becomes, \begin{gathered}x+x+2x-15+2x-15=360^\circ\\\\6x-30=360^\circ\\\\6x=360+30\\\\6x=390^\circ\\\\x=\dfrac{390}{6}\\\\x=65^\circ\end{gathered} x+x+2x−15+2x−15=360 ∘
6x−30=360 ∘
6x=360+30 6x=390 ∘
x= 6 390
x=65 ∘
other angle would be \begin{gathered}2x-15\\\\2(65)-15\\\\=130-15\\\\=115^\circ\end{gathered} 2x−15 2(65)−15 =130−15 =115 ∘
Hence, all the angles are 65°, 115°, 65°, 115°. |
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