Question

A triangle of sides of length 6 cm, 7 cm and 7 cm is constructed. Then the measure of the angle opposite to the side of length 6 cm is

• A. 27${}^{\circ }$
• B. 38${}^{\circ }$
• C. 51${}^{\circ }$
• D. 64${}^{\circ }$

Answer 1

The correct option is C

51${}^{\circ }$

Let us construct the required triangle as follows:

Step 1:
Draw the base line YZ of the length 7 cm.

Step 2:
Use your compass to make a circle with centre at point Y and the radius 6 cm.

Step 3:
Use your compass to make a circle with centre at point Z and the radius 7 cm.

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

Now, by above construction, we see that the angle opposite to the side of length 6 cm is $\angle$Z.

Using a protractor, we see that the measure of angle Z is 51${}^{\circ }$.