Question

Eric Drew an obtuse triangle. Which of the following could be true for Eric's triangle.

Answer 1

Answer:

Option:B 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.