Complete the statement, and find the value of x in the diagram. A trapezium with two opposite angles is labeled as 101 degrees.
1 answer:
The complete statement about the quadrilateral is, the quadrilateral shown is a kite and the value of x is 3
<h3>What are quadrilaterals?</h3>Quadrilaterals are shapes that have four sides and four angles.
The four sides may or may not be congruent, and at the same time the four angles may or may not be congruent
<h3>How to determine the value of x?</h3>The image that completes the question is added at the end of this solution as an attachment
From the attached figure, we have the following highlights
- Opposite angles of the quadrilateral are congruent
- Adjacent sides of the quadrilateral are congruent
This means that:
AD = DC
AB = BC
The quadrilateral shown is a kite
So, we have the following congruent angles:
ADB = CDB
Substitute the measure of both angles
11x = 9x + 6
Subtract 9x from both sides
3x = 6
Divide both sides by 2
x = 2
Hence, the complete statement about the quadrilateral is, the quadrilateral shown is a kite and the value of x is 3
Read more about quadrilaterals at:
#SPJ1
You might be interested in
Step-by-step answer:
Please refer to attached image.
1. Quad PQRS is cyclic (all vertices on the same circle), so opposite angles are supplementary, meaning
that
angles QPS and QRS are supplementary =>
QPS+QRS=180 =>
QRS = 180 - 74 = 106
2. Triangle RSQ is isosceles with RS=RQ =>
angles RSQ and RQS are congruent.
3. Angle RSQ = (180 - 106) /2 = 74 / 2 = 37
4. QP is a diameter => angle QSP is a right-angle.
5. From (3) and (4) above,
angle RSP = 37+90 = 127
6. Since PQRS is cyclic, angles RQP and RSP are supplementary =>
RQP+RSP = 180 =>
x + 127 = 180 =>
x = 180 - 127 = 53 degrees.
