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Since we know that <C is congruent to <E, we can say that: A. the two triangles are similar by SAS.
<h3>The properties of similar triangles.</h3>
In Geometry, two triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Ratio = BC/AC = 6/3 = 2.
Ratio = FE/DE = 4/2 = 2.
Thus, the ratio of their corresponding sides are equal in magnitude i.e BC/AC ≡ FE/DE.
Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.
Read more on congruency here: brainly.com/question/11844452
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(-3/1) * (1/-3) = 1
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Answer:
m<XUY = 40
Step-by-step explanation:
The central angles theorem states that in a circle, the measure of an angle with its vertex on the center of the circle is equal to the angle measure of the arc surrounding it. As a given fact, the sum of degree measures in a circle is (360) degrees. Thus, one can form the following equation:
(mZUV) + (mVUW) +(mWUX) +(mXUY) + (mYUZ) = 360
Substitute,
(-15x) + (30) + (90) + (x + 47) + (95) = 360
Simplify,
(-15x) + (30) + (90) + (x + 47) + (95) = 360
-14x + 262 = 360
Inverse operations,
-14x + 262 = 360
-14x = 98
x = -7
Substitute back into the equation for the measure of angle (<XUY)
m<XUY = x + 47
= -7 + 47
= 40
