A triangle has an angle that measures 105.6°. The other two angles are in a ratio of 14:17. What are the measures of those two angles?

2 Answers
Apr 26, 2018

#color(blue)(33.6^@)#

#color(blue)(40.8^@)#

Explanation:

All the angles in a triangle add to #180^@#, so the sum of the unknown angles is:

#180^@-105.6^@=74.4^@#

These are in a ratio of #14:17#

Add these:

#14+17=31#

Divide #74.4# by this:

#74.4/31#

Distribute this in the given ratio:

#14xx74.4/31=33.6#

#17xx74.4/31=40.8#

So the angles are:

#color(blue)(33.6^@)#

#color(blue)(40.8^@)#

The 2 angles are 33.6° and 40.8°.

Explanation:

We know, Sum of angles of a triangle = 180°
Also, if the angles are in the ratio 14:17, we know that the sum of the angles is #14x+17x#.
So, #180° =14x+17x+105.6° #
We can now simplify it, #180-105.6=31x#
#74.4/31=x#
#x=2.4#
Thus, #14x=2.4*14=33.6° #
And, #17x=2.4*17=40.8° #