Answer:
<u>Option:B</u> is the correct answer.
B: possible angle measures of the triangle are 92, 48, and 40
.
Step-by-step explanation:
We know that an obtuse triangle is a triangle whose one angle is a obtuse angle ( i.e. the measure of the angle is greater than 90 degree and less than 180 degrees).
A)
A: all three angles have equal measures
Let the angle of a triangle be 'x'.
As we know that the sum of all the angles of a triangle is 180°.
This implies that:
x+x+x=180°
3x=180°
⇒ x=60°
Hence, the triangle will not be obtuse as none of the angle is obtuse.
Hence, option: A is incorrect.
B)
possible angle measures of the triangle are 92, 48, and 40.
This option is correct.
Since there is one angle which is obtuse ( measure 92 degree)
and also such a angle measure is possible in a triangle as sum of all the angles is 180°.
( since 92+48+40=180°)
C)
two of the angles are equal, and the third angle has a measure of 70.
Let the equal angles be represented by 'x'.
As the sum of all the angles is 180°.
⇒ x+x+70=180°
⇒ 2x=110°
⇒ x=55°
Hence, here also none of the angle is obtuse.
hence, option: C is incorrect.
D)
One angle has a measure of 90, while, the other two angles measure less than 90°.
Such a triangle will not be a obtuse triangle as none of the angle measure is greater than 90°.
Hence, option: D is incorrect.
