Respuesta :

calculista

Answer:

The measure of angle ADC is 115°

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The quadrilateral ABCD is a isosceles trapezoid.

The properties of the isosceles trapezoid are as follows:

-The lower base angles are congruent.

-The upper base angles are congruent.

-Any lower base angle is supplementary to any upper base angle

So

m∠A=m∠D

m∠B=m∠C

m∠A+m∠B=180°

m∠D+m∠C=180°

therefore

m∠D=m∠A=115°

m∠B=180°-m∠A

m∠B=180°-115°

m∠B=65°

m∠C=m∠B=65°

The measure of angle ADC is 115°

Ver imagen calculista
lhmarianateixeira

In this exercise we want to calculate the value of the angle of the quadrilateral, so we find that:

The angle is 115°

We know that the quadrilateral in question is a trapeze and for that we have that some important properties of this figure are given as:

  • The lower base angles are congruent.
  • The upper base angles are congruent.
  • Any lower base angle is supplementary to any upper base angle

From this knowledge we can now calculate the value of the angle as:

[tex]m_A=m_D\\m_B=m_C\\m_A+m_B=180\\m_D+m_C=180\\m_D=m_A=115\\m_B=180-m_A\\m_B=180-115\\m_B=65\\m_C=m_B=65\\=115[/tex]

See more about trapeze at brainly.com/question/11600014

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