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△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 =

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 mKJL mKJL class=

Respuesta :

Answer:

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°.

shristiparmar1221

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°.

For more details, prefer this link:

https://brainly.com/question/25875846

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