△JKL and △LMN are shown. TrianglesJ K L and M N L share point L. Angle K measres 72 degrees. J K and K L are congruent. L M and L N are congruent.

What is m∠KJL?

m∠KJL =

This question is based on the concept of congruency. Therefore, the angle KJL is 54°.

Given:

Triangles J K L and M N L share point L. Angle K measures 72 degrees. J K and K L are congruent. L M and L N are congruent.

We need to determined the angle KJL.

According tot the question,

It is given that, in ΔJKL,  

⇒ ∠JKL = 72°

⇒ JK ≅ KL  ( Given )

Therefore, two sides of ΔJKL are congruent. So, the triangle is an isosceles triangle.

By using the property of an isosceles triangle,

Opposite angles of the congruent sides of an isosceles triangle are equal in measure.

Therefore,

⇒ ∠J ≅ ∠L

By the property of a triangle,

As we know that, sum of all interior angles of a triangle is 180°.

⇒∠J + ∠K + ∠L = 180°

⇒∠J + 72° + ∠J = 180° [Since, ∠J = ∠L]

⇒2 ∠J = 180° - 72°

⇒∠J = 54°

Therefore, ∠KJL or ∠J is 54°.

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m∠KJL = 54°

Step-by-step explanation:

In ΔJKL,

m∠JKL = 72°

JK ≅ KL

Since, two sides of ΔJKL are congruent, triangle is an isosceles triangle.

By the property of an isosceles triangle,

Opposite angles of the congruent sides of an isosceles triangle are equal in measure.

Therefore, ∠J ≅ ∠L

By the property of a triangle,

Sum of all interior angles of a triangle is 180°.

m∠J + m∠K + m∠L = 180°

m∠J + 72° + m∠J = 180° [Since, m∠J = m∠L]

2m∠J = 180° - 72°

m∠J = 54°

Therefore, m∠KJL or m∠J is 54°.

the answer is here: : )

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step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be