△BCE∼△JKL . If m∠B=89° , m∠C=13° , and m∠E=78° what is m∠J ?
M<j = ( )
m∠J = 180 - m∠K - m∠L (Triangle Angle Sum Theorem)
Since triangles BCE and JKL are similar, we can set up the proportion:
m∠BCE / m∠JKL = m∠C / m∠K = m∠E / m∠L
Substituting in the given angle measures:
89 / m∠JKL = 13 / m∠K = 78 / m∠L
To find m∠J, we need to find m∠L.
From the second proportion, we can solve for m∠K:
13 / m∠K = 78 / m∠L
13m∠L = 78m∠K
m∠L = 6m∠K
Substituting this back into the first proportion:
89 / m∠JKL = 13 / m∠K = 78 / (6m∠K)
Cross multiplying:
89 * m∠K = 13 * m∠JKL
m∠JKL = (89 * m∠K) / 13
Substituting this back into the second proportion:
13 / m∠K = 78 / (6 * (89 * m∠K) / 13)
13 * (6 * (89 * m∠K) / 13) = 78 * m∠K
6 * 89 * m∠K = 78 * m∠K
534m∠K = 78m∠K
534 = 78
This equation has no solution, which means the given angle measures do not form similar triangles. Therefore, it is not possible to determine m∠J.