∠A=6x−18 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 18, degrees, end color #1
1 answer:
Using the properties of alternate angles, the value of x = 8 and ∠ A = 30
<h3>What are Alternate Angles?</h3>A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (four total angles) of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal.
For the given question,
∠A=6x−18
∠B=14x+38
As, both parallel lines are intersected by a transversal,
the value of angle ∠A and ∠180 - B is same as they are alternate angles,
⇒ 6x−18 = 180 - 14x - 38
⇒ 6x + 14x = 142 + 18
⇒ 20x = 160
⇒ x = 8
∠A = 6x−18
⇒ ∠ A = 30
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The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
<h3>How to interpret the segments formed from Triangle Centroid?</h3>The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.
Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Read more about Triangle Centroid at; brainly.com/question/7644338
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