Question

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Answer 1

Answer: m∠D=15°

Step-by-step explanation:

Given: ΔDEF is similar to ΔJKL .

In addition,  m∠F=90° and m∠K=5(m∠D)

Let m∠D = a

Then,

∠D=∠J=a

∠E=∠K=5a

∠F=∠L=90°

Using Angle sum property, in triangle ΔDEF, we get

$\angle{D}+\angle{E}+\angle{F}=180^{\circ}\\\\\Rightarrow\ a+5a+90=180\\\\\Rightarrow\ 6a=90\\\\\Rightarrow\ a=15$

Hence, m∠D=15°

The angle sum property of a triangle says that, the sum of all the angles in a triangle is $180^{\circ}$.

Answer 2

Since triangle DEF = triangle JKL, m<D = m<J, m<E = m<K, m<F = m<L.
m<F = m<L = 90 degrees
m<K = m<E = 5(m<D)
but m<E + m<D = 90 degrees        [right angled triangle]
5(m<D) + m<D = 90 degrees
6(m<D) = 90 degrees
m<D = 90 / 6 = 15 degrees.