Question

question 5 of 10
which of the following words correctly describe a triangle with two 45°
angles?
check all that apply.
a. obtuse
b. right
c. equilateral
d. equiangular
e. isosceles
f. scalene

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the third angle

Given two angles are \(45^\circ\), let the third angle be \(x\). Then \(45^\circ + 45^\circ + x = 180^\circ\), so \(x = 180^\circ - 90^\circ = 90^\circ\).

Step3: Analyze each option

• A. Obtuse: An obtuse triangle has one angle \(> 90^\circ\). Here the largest angle is \(90^\circ\), so not obtuse.
• B. Right: A right triangle has one \(90^\circ\) angle. This triangle has a \(90^\circ\) angle, so it is right.
• C. Equilateral: Equilateral triangles have all angles \(60^\circ\). Here angles are \(45^\circ, 45^\circ, 90^\circ\), so not equilateral.
• D. Equiangular: Equiangular triangles have all angles equal. Here angles are not all equal, so not equiangular.
• E. Isosceles: An isosceles triangle has at least two equal angles. This triangle has two \(45^\circ\) angles, so it is isosceles.
• F. Scalene: A scalene triangle has all angles (and sides) different. Here two angles are equal, so not scalene.

Answer:

B. Right, E. Isosceles