What is the measure of ∠K?
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Answer:
The measure of angles of parallelogram are
∠A = 50° ,
∠B = 130° ,
∠C = 50° ,
∠D = 130°
Step-by-step explanation:
Given as for a parallelogram :
The vertices of parallelogram is A B C D in clockwise
The measure of angle A = ∠A = ( 2 x )°
The measure of angle B = ∠B = ( 5 x + 5 )°
Now, for a parallelogram , the sum of measure of all four angles = 360°
<u>From The property of Parallelogram</u>
A ) The adjacent angles are supplementary
So, ∠A + ∠B = 180°
Or, ( 2 x )° + ( 5 x + 5 )° = 180°
Or, ( 7 x + 5 )° = 180°
Or , ( 7 x )° = 180° - 5°
Or , ( 7 x )° = 175°
∴ x =
I.e x = 25°
So, ∠A = ( 2 x )° = ( 2 ×25° )
I.e , ∠A = 50°
∠B = ( 5 x + 5 )°
Or, ∠B = ( 5 ×25° + 5 )°
I.e , ∠B = 130°
B ) The opposite angles of parallelogram is equal
So, ∠C = ∠A = 50°
I,e ∠C = 50°
And ∠D = ∠B = 130°
I.e ∠D = 130°
Hence The measure of angles of parallelogram are ∠A = 50° , ∠B = 130° , ∠C = 50° , ∠D = 130° Answer