RBSE Solutions Class 8 Maths Chapter 7 Construction of Quadrilaterals Exercise 7.5

Question 1. Construct a quadrilateral MORE, in which MO = 6 cm., OR = 4.5 cm., ∠M = 60°, ∠O = 105° and ∠R = 105°.
Answer: First, we draw a rough outline of the quadrilateral with the given measurements to understand its shape.

Answer:

**Steps of Construction:**
(i) First, draw a line segment MO that is 6 cm long.
(ii) At point M, make an angle of 60° (∠OMX) with MO. At point O, make an angle of 105° (∠MOY) with MO. The rays for these angles will extend upwards.
(iii) From point O, use your compass to cut an arc of 4.5 cm along the ray OY. Mark this intersection point as R. This sets the length of the side OR.
(iv) Now, at point R, construct an angle of 105° (∠ORE) such that the ray from R (let's call it RZ) intersects the ray MX (from point M) at a point. Mark this intersection point as E.
(v) The figure MORE is the required quadrilateral. Each angle and side length fits the given conditions precisely.

In simple words: First, draw the base line. Then draw the angles from its ends. Mark the length of the next side. Finally, draw the last angle to complete the shape. This method helps build quadrilaterals step-by-step.

🎯 Exam Tip: Always start with a rough sketch to visualize the quadrilateral. Use a protractor for angles and a ruler for lengths to ensure accuracy in your construction.

Question 3. Construct a quadrilateral PQRS in which ∠P = 75°, ∠Q = 85°, ∠R = 110°, PQ = 4.1 cm. and QR = 3.9 cm.
Answer: Let's first draw a rough sketch to guide our construction of the quadrilateral PQRS.

Answer:

**Steps of Construction:**
(i) First, draw a line segment PQ, measuring 4.1 cm.
(ii) At point P, draw a ray PX such that it forms an angle of 75° (∠QPX) with PQ.
(iii) At point Q, draw a ray QY making an angle of 85° (∠PQY) with PQ. Then, from Q, cut an arc of 3.9 cm on ray QY and mark the point R. This defines the side QR.
(iv) At point R, draw a ray RZ that makes an angle of 110° (∠QRZ) with QR. Extend this ray until it intersects the ray PX (from point P) at a point. Mark this intersection point as S.
(v) The shape PQRS is the required quadrilateral, constructed using the given angle and side measures. This process ensures all properties are met.

In simple words: Start by drawing the first side and its angles. Then, measure and mark the second side. Finally, draw the last angle to connect all points and complete the shape. This systematic approach ensures accurate construction.

🎯 Exam Tip: When given three angles and two adjacent sides, extend rays and use the third angle to find the final vertex. Accuracy in angle measurement is key.

Question 4. Construct a quadrilateral DNSI, in which DN = 2.5 cm., NS = 3.7 cm. and ∠I = 60°, ∠N = 120°, ∠S = 90°.
Answer: Let's begin by sketching a rough diagram to visualize the quadrilateral DNSI with its given dimensions.

Answer:

**Steps of Construction:**
(i) First, draw a line segment NS, measuring 3.7 cm.
(ii) At point N, draw a ray NX making an angle of 120° (∠SNX) with NS. At point S, draw a ray SY making an angle of 90° (∠NSY) with NS. These rays will extend upwards.
(iii) From point N, use your compass to cut an arc of 2.5 cm along the ray NX. Mark this intersection point as D. This sets the length of the side DN.
(iv) Now, at point D, construct an angle of 60° (∠NDZ) with DN. Extend the ray DZ until it intersects the ray SY (from point S) at a point. Mark this intersection point as I.
(v) The figure DNSI is the required quadrilateral, successfully constructed using the given measurements. This method systematically builds the quadrilateral by ensuring each specified angle and side is correctly positioned.

In simple words: Start with the known base and its angles. Then, mark the length of the adjacent side. Finally, draw the third angle, making sure its ray meets the ray from the other base point to complete the shape. This systematic approach ensures the quadrilateral matches all given measurements.

🎯 Exam Tip: When three angles and two adjacent sides are given, it's often easiest to draw the base side, then the two adjacent angles, then cut the length of the second side, and finally use the third angle to complete the figure.