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triangle ABD shares a side with triangle BDC segment AD= 11 and segment DC= 8 angle ABD= 63 and angle CBD= (8x+7). segment AB = segment BC
what are the possible values of x?
In order to find the possible values of x, we need to apply the Angle Side Angle (ASA) congruence criterion.
1. First, let's identify the corresponding parts of the triangles ABD and BDC.
- Corresponding side: Segment AD in triangle ABD corresponds to segment CD in triangle BDC.
- Corresponding angle: Angle ABD in triangle ABD corresponds to angle CBD in triangle BDC.
2. We are given that segment AB is equal to segment BC. Therefore, triangle ABC is an isosceles triangle.
3. Based on the isosceles triangle, we can conclude that angle ABC is also equal to angle BAC.
4. Now, let's express angle CBD in terms of x.
- The given angle CBD = 8x + 7.
5. Since angles ABD and CBD are corresponding angles, they must be congruent.
- 63 = 8x + 7
6. Now, solve the equation for x.
- 63 - 7 = 8x
- 56 = 8x
- x = 7
Therefore, the possible value of x is 7.