If G is the incenter of triangle ABC, find each measure

Applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:

Recall the following facts about the incenter of a triangle:

The incenter of a triangle is the point where the three angle bisectors that divides each angle vertex into two intersect each other.

The incenter also, is a point equidistant to all three sides of the triangle at right angle.

Applying the properties above, the measures in the image can be calculated as shown below.

Find :

(angle bisector definition)

Find :

(angle bisector definition)

Find :

(sum of triangle definition)

Find :

(angle bisector definition)

Find DG:

(Perpendicular bisectors of the sides of a the triangle are equal in length from the incenter of a triangle)

Find BG:

(Pythagorean Theorem)

Find BE:

(Pythagorean Theorem)

Find GC:

(Pythagorean Theorem)

In summary, applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:

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m∠ABG = 20 degrees

m∠BCA = 22 degrees

m∠BAC = 118 degrees

m∠BAG = 59 degrees

DG = 4

BE = 12.4

BG = 11.7

GC = 20.4

Step-by-step explanation:

The given parameters are;

m∠CBG = 20°, m∠BCG = 11°

The incenter of a triangle is the point where the three bisectors of ΔABC meets

m∠ABG = m∠CBG = 20° by definition of angle bisector

m∠ABG = 20°

m∠ACG = m∠BCG = 11° by definition of angle bisector

m∠BCA = m∠ACG + m∠BCG = 11° + 11° = 22°

m∠ABC = m∠ABG + m∠CBG = 20° + 20° = 40°

m∠BAC = 180° - (m∠BCA+m∠ABC) = 180° - (40° + 22°) = 118°

m∠BAG = m∠CAG by definition of angle bisector

m∠BAC = 118° = m∠BAG + m∠CAG = m∠BAG + m∠BAG = 2 × m∠BAG

2 × mBAG = 118°

m∠BAG = 118°/2 = 59°

m∠BAG = 59°

Given that "G" is the incenter of the triangle ABC, we have;

GF = GE = DG = The radius of the incircle of the triangle = 4

Therefore, by Pythagoras' theorem, we have;

BG = √(11² + 4²) = √137 ≈ 11.7

BE = √((BG)² + 4²) = √(137 + 4²) = √153 ≈ 12.4

GC = √(20² + 4²) = √416= 4·√26 ≈ 20.4

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step-by-step explanation:

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answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column