Lucy drew an isosceles triangle as shown.
A triangle is shown with point Z at the lower left, point Y to the right and slightly up and point X to the upper right. Short line segments cross line segments Y Z and Y X.
If the measure of ∠YZX is 25°, what is the measure of ∠XYZ?
A. 50°
B. 75°
C. 130°
D. 310°
can't tell whether X is the vertex angle or one of the two base angles. Since all of the choices are integers, I'd say 180-(25+25) = 130
To find the measure of angle ∠XYZ, we can use the fact that the sum of the interior angles of a triangle is 180°. Since it is an isosceles triangle, we know that angles ∠YZX and ∠YXZ are congruent. Let's represent the measure of angle ∠XYZ as x.
Given that ∠YZX is 25°, we can set up the equation:
x + 25° + x = 180°
Combining like terms:
2x + 25° = 180°
Next, let's solve for x by subtracting 25° from both sides of the equation:
2x = 180° - 25°
2x = 155°
Now, let's divide both sides of the equation by 2 to isolate x:
x = 155° / 2
x = 77.5°
Therefore, the measure of angle ∠XYZ is approximately 77.5°.
Since none of the answer choices match 77.5° exactly, we can round it to the nearest whole number.
Therefore, the answer is (B) 75°, which is the closest whole number to 77.5°.
To find the measure of ∠XYZ, we need to use the fact that the angles of a triangle add up to 180 degrees.
We know that ∠YZX is 25°. Since the triangle is isosceles, we know that ∠YZX is also equal to ∠YXZ.
Therefore, the sum of ∠YZX and ∠YXZ is 25° + 25° = 50°.
Since the sum of all three angles of a triangle is 180°, we can find ∠XYZ by subtracting the sum of ∠YZX and ∠YXZ from 180°.
∠XYZ = 180° - (∠YZX + ∠YXZ)
= 180° - (50°)
= 130°
Therefore, the measure of ∠XYZ is 130°.
So, the answer is C. 130°.