Triangle CAT

magentarita · #1 $Old$ December 2nd, 2008, 11:50 PM

In isosceles triangle CAT, the measure of the vertex angle is one-half the
measure of one of the base angles. Which statement is true about ΔCAT?

(1) ΔCAT is an equilateral triangle.
(2) ΔCAT is an acute triangle.
(3) ΔCAT is a right triangle.
(4) ΔCAT is an obtuse triangle.

great_math · #2 $Old$ December 2nd, 2008, 11:58 PM

Let the base angles are 2x and 2x so the angle at the vertex=x

$2x+2x+x=180^0$

$5x=180^0$

$x=36^0$

$2x=72^0$

So angles are $72^0,72^0,36^0$

So it is a ...... Acute triangle

magentarita · #3 $Old$ December 3rd, 2008, 07:37 PM

Quote:

Originally Posted by great_math $View Post$

Let the base angles are 2x and 2x so the angle at the vertex=x

$2x+2x+x=180^0$

$5x=180^0$

$x=36^0$

$2x=72^0$

So angles are $72^0,72^0,36^0$

So it is a ...... Acute triangle

Great work, brother.