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Viefleur [7K]
3 years ago
13

If an angle of a parallelogram is two-third of

Mathematics
1 answer:
balandron [24]3 years ago
5 0

Answer:

We know that in a parallelogram two opposite angles are equal -

\\  \implies \sf \: 2x + 2y = 360 {}^{ \circ}  \\  \\  \\  \implies \sf \: x + y = 180 {}^{ \circ}  \qquad \quad \: (i) \\

<u>Given</u><u> </u><u>-</u><u> </u>

  • angle x is equal to the two - third of it's adjacent angle y.

\\  \implies \sf \: x =  \frac{2}{3} y \\  \\  \\  \implies \sf \frac{x}{2}   =  \frac{y}{3}  = k \\  \\  \\  \qquad \sf \small \underline{ x = 2k \:   \: \& \:  \: y = 3k} \\

Now, by using equation (1) :

\\  \implies \sf \: 2k + 3k = 180 \\  \\  \\  \implies \sf \: 5k = 180 \\  \\  \\  \implies \sf \: k =  \frac{180}{5}  \\  \\  \\   \large{ \boxed{ \sf{k =  {36}^{ \circ} }}} \\

<u>Now</u><u>,</u><u> </u><u> </u><u>by</u><u> </u><u>putting</u><u> </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>k</u><u> </u><u>in</u><u> </u><u>x</u><u> </u><u>and</u><u> </u><u>y</u><u>.</u><u> </u>

  • x = 2k = 2 × 36 = 72°
  • y = 3k = 3 × 36 = 108°

<u>Therefore</u><u>,</u><u> </u><u>the</u><u> </u><u>right</u><u> </u><u>option</u><u> </u><u>and</u><u> </u><u>small</u><u>est</u><u> </u><u>angl</u><u>e</u><u> </u><u>is</u><u> </u><u>b</u><u>)</u><u> </u><u>7</u><u>2</u><u>°</u><u>.</u>

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