Construct a quadrilateral ABCD, give that AB=5cm, BC=4cm, `/_B=70^(@),/_A=90^(@)` and `/_C=150^(@)`

Answer

To construct the quadrilateral ABCD with the given dimensions and angles, follow these steps:

### Step 1: Draw Line Segment AB
- Draw a line segment AB that measures 5 cm.
- Label the endpoints as A and B.

### Step 2: Construct Angle B
- At point B, use a protractor to measure an angle of 70 degrees.
- Mark this angle with a point (let's call it point C) such that the angle opens away from line AB.

### Step 3: Draw Line Segment BC
- From point B, draw a line segment BC that measures 4 cm.
- Mark the endpoint as C.

### Step 4: Construct Angle A
- At point A, use a compass to construct a 90-degree angle.
- To do this, draw an arc from point A that intersects line AB, then use the intersection points to create the right angle.

### Step 5: Draw Line Segment AD
- From point A, draw a line along the 90-degree angle until it intersects with the line that will be drawn from point C.

### Step 6: Construct Angle C
- At point C, construct an angle of 150 degrees using the protractor.
- Mark this angle and extend the line until it intersects with the line drawn from point A.

### Step 7: Mark Point D
- The intersection of the lines from points A and C will be point D.
- Label the intersection point as D.

### Step 8: Complete the Quadrilateral
- Connect points A, B, C, and D to form quadrilateral ABCD.

### Final Step: Review the Construction
- Ensure all measurements and angles are correct and that the quadrilateral is properly formed.

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