Question

find the measure of all the angles of a parallelogram if one angle is 15 degree less than twice the smallest angle

Answer 1

15 +x-2 +15 +x-2=360
30+2x-4=360
26+2x=360
2x=360-26
2x=234
x=234÷2
x= 117

Answer 2

Answer: 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

$2x-15$

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,

$x+x+2x-15+2x-15=360^\circ\\\\6x-30=360^\circ\\\\6x=360+30\\\\6x=390^\circ\\\\x=\dfrac{390}{6}\\\\x=65^\circ$

other angle would be

$2x-15\\\\2(65)-15\\\\=130-15\\\\=115^\circ$

Hence, all the angles are 65°, 115°, 65°, 115°.