Question

A triangle of sides EF = 2.5 cm, DF = 2 cm and DE = 4 cm is constructed. Then measure of angle F

• A. is 90${}^{\circ }$
• B. lies between 90${}^{\circ }$ and 150${}^{\circ }$
• C. is greater than or equal to 150${}^{\circ }$
• D. less than 90${}^{\circ }$

Answer 1

The correct option is B

lies between 90${}^{\circ }$ and 150${}^{\circ }$

Step 1:
Draw the base line DE of the length 4 cm.

Step 2:
Use your compass to make a circle with centre at point D and the radius 2 cm.

Step 3:
Use your compass to make a circle with centre at point E and the radius 2.5 cm.

Step 4:
In the point of intersection between the two circles, you'll find the point F.
Complete the triangle by drawing the lines between all three points, as shown below.

Now, by above construction, we see that the measure of angle F is 125${}^{\circ }$.

Hence option (b) is the correct one.