It's an isosceles triangle so angles A and BCA are congruent.
Angle BCA is the supplement of BCD, so 180-109 = 71.
Angle A is congruent to that, so A=71 degrees.
Let's see if we can get that in the format they want, kind of as a proof.
1. ∠BCD=109° Reason: Given
2. AB ≅ BC Reason: Given
3. ∠BCA = 71° Reason: Linear pairs are supplementary
4. ΔABC is isosceles. Reason: Definition of isosceles
5. ∠A ≅ ∠BCA Reason: Isoceles triangle theorem
6. ∠A = 71° Reason: Def congruent
Answer: 71 degrees
9514 1404 393
Answer:
- reflection across the origin
- rotation 180° about the origin
- reflection across the x-axis, and translation right 6 units
Step-by-step explanation:
The figure and its image are symmetrical about the origin, so the following three transformations are equivalent:
1. reflection across the origin
2. rotation 180° about the origin
3. reflection across both x- and y-axes, in either order
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The figure itself has left-right symmetry, so only one reflection is necessary to map the figure to its image: reflection across a horizontal line. Following that reflection, the image can be put into place by an appropriate translation. One such pair of transformations is ...
4. reflection across the x-axis and translation 6 units right, in either order
Step-by-step explanation:
Ratio of length to width = 7 : 4
length = 7x
width = 4x
7x + 4x = 11x
length = 880
width = 4x
= 4(125.71)
= 502.85
