Question

A quadrilateral has congruent side lengths. 2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees. What is the value of x? 14 15 16 17

Answer 1

x = 14.

Explanation:

The other 2 opposite angle are both equal to 70 degrees.

So 5x = 70

x = 70/5

= 14 degrees.

Answer 2

Option A.

Explanation:

It is given that a quadrilateral has congruent side lengths. It means the quadrilateral is either square of rhombus.

Each interior angles of a square is a right angle.

2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees.

Since the interior angles of the given quadrilateral are not right angles, therefore it must be a rhombus.

Opposite angles of a rhombus are congruent.

`5x=70`

Divide both sides by 5.

`x=(70)/(5)`

`x=14`

The value of x is 14.

Therefore, the correct option is A.