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Kumar and Akhil work at the same office. They start for office from their homes at \(B\) and \(C\), respectively, to reach office \(A\). Two roads, \(D\) and \(E\), meets the roads \(AB\) and \(AC\), and \(DE\) is parallel to \(BC\). Their paths to office form a triangular shape, as shown below.
1. If \(AE =\) 5 \(kms\), \(EC =\) 2 \(kms\) and \(DB =\) 6 \(kms\), then the length of \(AD\) is \(kms\).
2. If \(AD =\) 5 \(kms\), \(AE =\) 15 \(kms\) and \(AC =\) 24 \(kms\), then the length of \(AB\) is \(kms\).
3. The perimeter of two similar triangles \(ABC\) and \(ADE\) are 37 \(kms\) and 19 \(kms\). If one side of \(\triangle ABC\) is 8 \(km\), then the corresponding side of \(\triangle ADE\) is \(kms\).
4. If \(\angle ADE = 48^{\circ}\) and \(\angle C = 80^{\circ}\), then the measure of \(\angle A\) is
5. Is \(DE \parallel BC\) if \(AD = 15 \ kms\), \(AE =\) 5 \(kms\), \(EC =\) 2 \(kms\) and \(DB =\) 6 \(kms\)?
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