Question

Question 1 3 pts In triangle ABC, the measure of angle A is 40 degrees. a.) Which pair are possible measures for angles B and C if triangle ABC is isosceles? Select two possible pairs. Select | and Select b.) Which pair are possible measures for angles B and C if triangle ABC is right? Select)

Answer 1

B.

The measure of angle of angle A is 40 degree.

In right angle triangle one angle is one angle is 90 degree.

In triangle sum of all three angle is 180 degree.

Determine the measure of third angle by using angle sum property of triangle.

`\begin{gathered} \angle A+\angle B+\angle C=180 \\ 40+90+\angle C=180 \\ \angle C=180-130 \\ =50 \end{gathered}`

So meansure of angle B and angle C is 90 degree and 50 degree.

Answer: 90 degree and 50 degree.

A.

In isoceles triangle, two angle are of equal measure.

If we assume two angles are equal to 40 degree.

Determine the measure of third angle by using angle sum property of triangle.

`\begin{gathered} 40+40+\angle C=180 \\ \angle C=180-80 \\ =100 \end{gathered}`

So a possible pair of two angle measure is 40 degree and 100 degree.

If we assume two remaining angles are equal and one angle is equal to 40 degree.

Determine the measure of two equal angles (angle B = angle C) by using angle sum property for triangle.

`\begin{gathered} \angle B+\angle C+40=180 \\ 2\angle B=180-40 \\ \angle B=(140)/(2) \\ =70 \end{gathered}`

So second possible pair of angle is 70 degree and 70 degree.