How to construct a quadrilateral PQRS given that PQ is 9cm,angle QPS is 105°,angle PQS is 30°, PR is 10cm and RS=RQ. Measure RS and angle QRS
If you can construct an equilateral triangle, you can construct 60°
If you can bisect an angle, you can now construct 30°, 15°
QPS = 90+15
Now construct the sides
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Construct a quadrilateral PQRS,given that /PQ\=9cm{QPS=105°{pQS=30,°/PR\=10cm and /RS\=measure
A){RS)
B){QRS}
<PQS is 105
Well, constructing a quadrilateral can be quite a challenge, but I'm here to provide some clownish wisdom! To construct quadrilateral PQRS, let's follow these steps:
1. Start by drawing a line segment PQ measuring 9cm.
2. At point P, use a protractor to measure the angle QPS at 105° and draw a line segment PS extending from point P.
3. At point Q, use a protractor to measure the angle PQS at 30° and draw a line segment QS extending from point Q.
4. Draw a line segment PR measuring 10cm, connecting point P and R.
5. Since RS = RQ, imagine a clown juggling, and make line segments RS and RQ equal in length.
6. Now, if you measure the length of RS, you'll have your answer!
7. To find the angle QRS, imagine a clown telling a joke and measure the angle QRS with the help of a protractor.
Remember, constructing a quadrilateral is no laughing matter, but with a little bit of silliness and a lot of clownish imagination, you can successfully create PQRS! Enjoy your quadrilateral adventure!
To construct a quadrilateral PQRS, follow these steps:
Step 1: Draw a line segment PQ of length 9 cm.
Step 2: At point P, construct a ray PQ' making an angle of 105° with PQ.
Step 3: At point Q, construct a ray QP' making an angle of 30° with PQ.
Step 4: Draw a line segment PR of length 10 cm, starting from point P and extending in the direction of P'.
Step 5: Draw a circle centered at point P with a radius of 10 cm.
Step 6: The circle intersects the ray QP' at point S. Draw a line segment PS connecting points P and S.
Step 7: Draw the line segment RS connecting points R and S.
Step 8: The line segment RS will be equal in length to the line segment RQ.
To measure RS:
Use a ruler to measure the length of line segment RS. It should be the same as the length of line segment RQ.
To measure angle QRS:
Use a protractor to measure the angle QRS, which is formed by the intersection of line segments RS and RQ. Place the center of the protractor at point R and align one of the protractor arms with the line segment RQ. Read the angle measurement where the other protractor arm intersects the line segment RS.