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akposevictor

Applying the properties of Isosceles triangle and the sum of triangle theorem, the values of x and y in the image given are:

[tex]x = 90^{\circ}\\\\y = 47 ^{\circ}[/tex]

Recall the properties of Isosceles Triangle:

An isosceles triangle has equal base angles an two equal legs that are opposite the base angles.

Triangle ABC is an isosceles triangle.

  • Therefore:

m<ACD = m<ABD = 47 degrees

Find y:

[tex]y = \frac{1}{2} (180 - (m \angle ACD + m \angle ABD))[/tex]

  • Substitute

y = 1/2(180 - (47 + 47))

y = 43 degrees.

Find x:

x = 180 - (y + m<ABD)

  • Substitute

x = 180 - (43 + 47) (sum of triangle)

x = 90 degrees

Therefore, applying the properties of Isosceles triangle and the sum of triangle theorem, the values of x and y in the image given are:

[tex]x = 90^{\circ}\\\\y = 47 ^{\circ}[/tex]

Learn more here:

https://brainly.com/question/15214190

MrRoyal

Angles in a triangle may or may not be congruent.

The values of x and y are 90 and 47, respectively.

From the figure, we have:

[tex]\mathbf{AD \perp BC}[/tex]

This means that, angle x is a right-angle.

So, we have:

[tex]\mathbf{x = 90}[/tex]

Triangle ABC is an isosceles triangle.

So, we have:

[tex]\mathbf{\angle B = \angle C = 47}[/tex]

The measure of y is then calculated as:

[tex]\mathbf{y + \angle B + x = 180}[/tex] --- sum of angles in a triangle

This gives

[tex]\mathbf{y + 47 + 90 = 180}[/tex]

[tex]\mathbf{y + 137 = 180}[/tex]

Subtract 137 from both sides

[tex]\mathbf{137 = 43}[/tex]

Hence, the values of x and y are 90 and 47, respectively.

Read more about triangles at:

https://brainly.com/question/22227896

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