Explanation?

The sum of all 4 angles must be 360° and the opposite angles are equal.

You are told that B and D are 46° each:

A + B + C + D = 360

A + 46 + C + 46 = 360

A + C + 92 = 360

A + C = 268

Since A and C are equal:

x + x = 268

2x = 268

x = 134°

Angles A and C are 134°.

Sum of the internal angles of a closed polygon is 360°.

Opposite angles of a parallelogram are equal.

B = D = 46

A = C = [360 - 2(46)]/2

C = 180-46 = 134°

ANS: C = 134°

In a parallelogram, opposite angles are congruent and adjacent angles are supplementary.

Since m∠B = m∠D = 46°, the adjacent angles (∠A and ∠C) must be supplementary (add to 180°)

46° + m∠C = 180°

m∠C = 180° - 46°

m∠C = 134°