Preview Question : MT-07-09-03-03-Q01

The diagram below shows two parallelograms, \(DEFG\) and \(HGJK\). \(DGJ\) and \(FGH\) is the straight line.

Find the value of \(x\).

(A) \(95\degree\)

(B) \(100\degree\)

(D) \(115\degree\)

Answer: C

The value of \(x\) is:

\(\begin {aligned}\angle DEF+75\degree&=180\degree\\\angle DEF&=180\degree-75\degree\\\angle DEF&= 105\degree.\end{aligned}\)

The opposite angles in a parallelogram are the same, then:

\(\angle DEF= \angle DGF= 105\degree.\)

Vertically opposite angles are the same, then:

\(\angle HGJ= \angle DGF= 105\degree.\)

The opposite angles in a parallelogram are the same.

\(\angle HKJ = \angle HGJ= 105\degree.\)

Then, the value of \(x\) = \(105\degree.\)