Question

unit 1, lesson 15: adding the angl
practice problems

1. in triangle abc, the measure of angle a is 40°. give possible measures for angles b and c if
2. give possible measures for angles b and c if
3. for each set of angles, decide if there is a triangle with measures in degrees:
4. 60, 60, 60
5. 90, 90, 45
6. 30, 40, 50
7. 90, 45, 45
8. 120, 30, 30

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is always $180^{\circ}$. That is, for $\triangle ABC$, $\angle A+\angle B+\angle C = 180^{\circ}$.

Step2: Solve Question 1

Given $\angle A = 40^{\circ}$, then $\angle B+\angle C=180^{\circ}-\angle A=180 - 40=140^{\circ}$. So any two non - negative angles $B$ and $C$ such that $B + C = 140^{\circ}$ are possible measures for angles $B$ and $C$ in $\triangle ABC$.

Step3: Solve Question 2

For each set of angles, add them up. If the sum is $180^{\circ}$, a triangle with those angle measures exists; if the sum is not $180^{\circ}$, a triangle with those angle measures does not exist. For example, for the set $60,60,60$, $60 + 60+60=180^{\circ}$, so a triangle exists. For the set $90,90,45$, $90 + 90+45=225^{\circ}
eq180^{\circ}$, so a triangle does not exist.

Answer:

Question 1:

There are infinite possible pairs of measures for angles $B$ and $C$ as long as $B + C=140^{\circ}$ (since the sum of the interior angles of a triangle is $180^{\circ}$ and $\angle A = 40^{\circ}$). For example, $B = 60^{\circ},C = 80^{\circ}$; $B=50^{\circ},C = 90^{\circ}$ etc.

Question 2:

1. Yes. Since $60 + 60+60=180^{\circ}$, a triangle with angle - measures $60^{\circ},60^{\circ},60^{\circ}$ exists (it is an equilateral triangle).
2. No. Because $90 + 90+45=225

eq180^{\circ}$, a triangle with these angle - measures does not exist.

1. No. Since $30 + 40+50 = 120

eq180^{\circ}$, a triangle with these angle - measures does not exist.

1. Yes. As $90 + 45+45=180^{\circ}$, a triangle with angle - measures $90^{\circ},45^{\circ},45^{\circ}$ exists (it is a right - isosceles triangle).
2. Yes. Since $120+30 + 30=180^{\circ}$, a triangle with angle - measures $120^{\circ},30^{\circ},30^{\circ}$ exists (it is an isosceles triangle).