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1 answer:
Considering that angles A and C are equal, and the sum of the internal angles of a triangle is 180º, we have that:
The measure of angle A is of: 48º.
The measure of angle B is of: 84º.
The measure of angle C is of: 48º.
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- Segments AC and CB have the same length, thus, angles A and C have the same measure, and then:
The measure of angle A is of: 48º.
The measure of angle C is of: 48º.
The<u> sum of the internal angles of a triangle is of 180º</u>, and this is used to find the measure of angle B.
The measure of angle B is of: 84º.
A similar problem is given at brainly.com/question/13216436
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Answer:
Therefore
1. Vertical Opposite Angle Theorem is used to prove that the triangles are similar.
2. Angle-Angle similarity statement is used.
3. x = 10 unit and y = 7.5 unit.
Step-by-step explanation:
Given:
∠A ≅ ∠E
AB = 8 , DE = 12 , BC = 5 , CE = 15
To Prove:
Δ ABC ~ ΔEDC
To Find :
x = ?
y = ?
Proof:
Vertical Angle Theorem:
The angles opposite each other when two lines cross. They are always equal.
Here vertical opposite angles are,
∴ ∠ACB ≅ ∠ECD
Angle-Angle Similarity :
If in Two triangle Two corresponding angles are congruent then the Triangles are Similar by Angle-Angle Similarity statement.
Now,
In Δ ABC and Δ EDC
∠A ≅ ∠E …………..{ Given }
∠ACB ≅ ∠ECD ……….....{Vertical Opposite Angle Theorem}
Δ ABC ~ Δ EDC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
On Substituting the given values we get
Therefore,
Therefore
1. Vertical Opposite Angle Theorem is used to prove that the triangles are similar.
2. Angle-Angle similarity statement is used.
3. x = 10 unit and y = 7.5 unit.
The answer is 7.21...
