Owen is measuring the angles of a triangle. He knows that two of the angles have the same measure and the third angle has a measure of 100°. What is the measure of the other two angles?
Responses
A 80°80°
B 130°130°
C 40°40°
D 260°
Let x be the measure of each of the two equal angles.
We know that the sum of the angles in a triangle is 180°:
x + x + 100 = 180
Simplifying:
2x + 100 = 180
2x = 80
x = 40
Therefore, each of the equal angles has a measure of 40°.
Answer: C) 40°40°
To find the measure of the other two angles in the triangle, we can use the fact that the sum of all the angles in a triangle is equal to 180°.
Let's call the measure of the two angles that are the same x.
So, the equation is: x + x + 100° = 180°
Combine the like terms: 2x + 100° = 180°
Subtract 100° from both sides: 2x = 80°
Divide both sides by 2: x = 40°
Therefore, the measure of the other two angles is 40°. So the correct answer is C) 40°40°.