Question

In circle A, ∠BAE ≅ ∠DAE.

Circle A is shown. Line segments A B, A E, and A D are radii. Lines are drawn from point B to point E and from point E to point D to form secants B E and E D. Angles B A E and E A D are congruent. The length of B E is 3 x minus 24 and the length of E D is x + 10.

What is the value of x?

14
17
27
34

Answer 1

Based on the definition of congruent triangles, the value of x is: B. 17.

What are Congruent Triangles?

Congruent triangles are triangles having corresponding angles and sides that are congruent to each other.

The two triangles in the diagram are equal.

• Therefore:

BE = ED

• Substitute

3x - 24 = x + 10

• Combine like terms

3x - x = 24 + 10

2x = 34

• Divide both sides by 2

x = 17

Therefore, based on the definition of congruent triangles, the value of x is: B. 17.

Learn more about congruent triangles on:

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Answer 2

Answer:

17

Step-by-step explanation: