Quadrilateral WXZY is a square. If YX = 30 and WT = 2x – 7, then find the value of x.
(Points : 2)
4
18.5
11
15
or
Quadrilateral JKLM is a rhombus. The diagonals intersect at N. If the measure of angle JKL is 104o, find the measure of angle JKN.
(Points : 2)
52°
104°
26°
76°
If by WT you mean WZ, the since the diagonals of a square are equal,
30 = 2x-7
2x = 37
x = 18.5
For the second one, remember that the diagonals of a rhombus bisect the corner angles.
So, JKN = LKN = 52°
Quadrilateral WXZY is a square. If YX = 30 and WT = 2x – 7, then find the value of x.
To find the value of x in the first question, we need to use the fact that square WXZY has four equal sides.
Given that YX = 30, we know that all sides of the square are equal to 30.
We are also given that WT = 2x – 7. Since the opposite sides of a square are parallel, we can say that WT is also equal to 30.
So, we have the equation 2x – 7 = 30.
To solve for x, we add 7 to both sides of the equation:
2x – 7 + 7 = 30 + 7
2x = 37
Finally, we divide both sides by 2 to isolate x:
2x/2 = 37/2
x = 37/2
Therefore, the value of x is 18.5.
For the second question, we need to find the measure of angle JKN in rhombus JKLM.
In a rhombus, all sides are equal and opposite angles are congruent.
Given that angle JKL is 104°, we can determine that angle JKN is half of angle JKL.
So, angle JKN = 104° / 2 = 52°.
Therefore, the measure of angle JKN is 52°.