1 Solve for x in the triangle below. Show your work! 2 84 Xº Y N

Mathematics

1 answer:

Alexus [3.1K]2 years ago

6 0

Answer:

x = 48°

Step-by-step explanation:

In the given triangle XYZ,

Sides XY and XZ are congruent.

Therefore, both the sides will be equal in measure.

By the definition of isosceles triangle,

"Opposite angles of the equal sides are equal in measure"

m∠Y = m∠Z = x°

m∠X = 84° [Given]

By the triangle sum theorem,

m∠X + m∠Y + m∠Z = 180°

84° + x° + x° = 180°

2x = 180 - 84

x = 48°

Therefore, measure of x = 48° will be the answer.

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4 0

2 years ago

Secants AC and DB intersect at point E inside the circle. Given that the measure of arc CD = 40o, arc AB = 60o, and arc BC = 160

s344n2d4d5 [400]

Answer:

C. $130^{\circ}$

Step-by-step explanation:

Please find the attachment.

We have been given that secants AC and DB intersect at point E inside the circle. Given that the measure of arc $CD = 40^o$ , arc $AB = 60^o$ , and arc $BC = 160^o$ . We are asked to find the measure of angle AED.

We know that the measure of angle formed by two intersecting secants is half the sum of measure of the arcs by intercepted by the angle and its vertical angle.

$\angle AED=\frac{\widehat{BC}+\widehat{AD}}{2}$