Question

In a parallelogram ABCD find the measure of all the angles if one of its angle is 15° less than twice the smallest angle​

Answer 1

Answer:

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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°.