The point N is in the center of triangle JKL
Step-by-step explanation:
The incenter of a triangle can be defined as the intersection of three angle bisectors that bisect all angles of the triangle.
By definition, an angle bisector divides an angle into two equal smaller angles.
Therefore:
What we're given:
The sum of the interior angles of a triangle always add up to be 180 degrees. Since these six angles make up the total sum of the interior angles, we have the following equation:
Substituting given values:
Since ,
Step-by-step explanation:
The incenter of a triangle can be defined as the intersection of three angle bisectors that bisect all angles of the triangle.
By definition, an angle bisector divides an angle into two equal smaller angles.
Therefore:
What we're given:
The sum of the interior angles of a triangle always add up to be 180 degrees. Since these six angles make up the total sum of the interior angles, we have the following equation:
Substituting given values:
Since ,
Check explanation section (check the attached file for the diagram to the question).
Step-by-step explanation:
Without mincing words let's dive straight into the solution to the question/ problem above.
From the question above, we have that the point p = the point at which the bisecting angle of the triangles meets, that is the term known as incenter.
So, we have that; 7x - 6 = 5x + 4. Hence;
2x = 10; x = 5°.
Thus, the angle 5x + 4 = which is the angle KJP = 5x + 4. Recall from above that x = 5°.
Hence; 5x + 4 = 5(5) + 4 = 25 - 4 = 29°.
Also, the angle 7x - 6 = which is the angle KJP = 7x - 6. Recall from above that x = 5°.
Therefore, 7x - 6 = 7(5) - 6 = 35 - 6 = 29°.
The angle KJP + the angle LJP= the angle KJL.
Therefore, the angle KJL = 29° + 29° = 58°.
Angle KJL = 130 - ( angle KJL) - (angle KJL).
The angle KJL = 130° - ( 58°) - (52° ) = 70°
By using the property of incenter, measures of the sides and the angles will be,
JK = 21.2 units
KL = 26.63 units
JL = 28.33 units
m∠K = 36°
By the property of incenter,
PM = PN = PO = 7 units
∠MJP = ∠OJP = 32°
∠NLP = ∠OLP = 22°
By the triangle sum theorem,
m∠JKL + m∠KLJ + m∠LJK = 180°
2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°
2(m∠NKP) + 2(22°) + 2(32°) = 180°
2(m∠NKP) = 180° - 108°
m∠NKP = 36°
From ΔJMP,
tan(32°) =
tan(32°) =
MJ =
MJ = 11.20
From ΔPOL,
tan(22°) =
tan(22°) =
OL = 17.33
From ΔKNP,
tan(36°) =
tan(36°) =
KN = 9.63
Therefore, JK = MJ + MK = 21.2 units
KL = LN + KN = 26.63 units
JL = JO + OL = 28.33 units
Learn more,
link
m∠JKP = 31.5°
Step-by-step explanation:
Incenter of a triangle is the point where all the bisectors of interior angles intersect each other.
JN is the angle bisector of ∠KJL.
Therefore, m∠KJN = m∠LJN
(7x - 6) = (5x + 4)
7x - 5x = 6 + 4
2x = 10
x = 5
m∠KJN = (7x - 6)
= 7(5) - 6
= 35 - 6
= 29°
In ΔKJN,
m∠JKN + m∠KNJ + m∠NJK = 180°
m∠JKN + 90° + 29° = 180°
m∠JKN = 180°- 119° = 61°
Since KO is the angle bisector of ∠JKN,
m∠JKP =
=
= 30.5°
The point N is in the center of triangle JKL
It will provide an instant answer!