Question

The second angle of a triangular kite is four times as large as the first. The third angle is 55 degrees ° more than the sum of the other two angles. Find the measure of the second angle

Answer 1

50 degrees

Explanation:

As the kite is triangular, the sum of all angles will be 180 degrees.

Let x be the first angle.

Then according to the statement second angle is four times as large as the first, second angle will be:

4x

And according to the statement, the third angle is 55 degrees ° more than the sum of the other two angles, third angle will be:

x+4x+55

So,

x+4x+x+4x+55=180

10x+55=180

10x= 180-55

10x=125

x=125/10

x=12.5 degrees

So first angle is 12.5 degrees.

Second angle = 4(12.5)

=50 degrees

Third angle = x+4x+55

= 12.5+50+55

= 117.5 degrees

To check if the sum of angles is 180 degrees

= 12.5+117.5+50 = 180

Hence, second angle is 50 degrees ..