Thread: quadrilateral question.

I'm stumped about this problem, any help would be super appreciated. Thanks.

The lengths of three consecutive sides of a quadrilateral are equal. If the angles included between these sides have measures of 60˚ and 70˚, what is the measure of the largest angle of the quadrilateral? Draw your figure.

Originally Posted by carla5980

I'm stumped about this problem, any help would be super appreciated. Thanks.

The lengths of three consecutive sides of a quadrilateral are equal. If the angles included between these sides have measures of 60˚ and 70˚, what is the measure of the largest angle of the quadrilateral? Draw your figure.

Draw a horizontal line of any length x.
Draw another line of length x off at 60 degrees
and another line of length x from the other end of the horizontal line at 70 degrees.

Join the corner with the 70 degree angle to the end of the other line.
Since 2 sides are x and the angle between the sides is 60 degrees,
this is a special case of isosceles triangle.
It's equilateral.

Now we have 4 lines of length x.
Hence the angles of the "thin" isosceles triangle are 10, 85, 85.
Therefore the largest angle is 85+60 degrees.

Try drawing it!