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10. In the given figure, ABCD is an isosceles trapezoid.
AB = DC, AD || BC, m(2DBC) = 22 and m(LACD) = 34
What is m(BAC)?

10 In the given figure ABCD is an isosceles trapezoid AB DC AD BC m2DBC 22 and mLACD 34 What is mBAC class=

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semsee45

Answer:

m∠BAC = 102°

Step-by-step explanation:

Properties of an Isosceles Trapezoid

  • Bases are parallel.
  • Legs (non-parallel sides) are equal in length.
  • Lower base angles are congruent.
  • Upper base angles are congruent.
  • Diagonals are equal in length.
  • Opposite angles are supplementary (sum to 180°).

As the base angles are congruent, AB = DC and AD ║ BC then:

⇒ m∠ABC = m∠DBC = 22°

⇒ m∠DBA = m∠ACD = 34°

Therefore,

⇒ m∠ABC = m∠DBA + m∠DBC

⇒ m∠ABC = 34° + 22°

⇒ m∠ABC = 56°

Angles in a triangle sum to 180°. Therefore:

⇒ m∠ABC + m∠BCA + m∠BAC = 180°

⇒ 56° + 22° + m∠BAC = 180°

⇒ 78° + m∠BAC = 180°

⇒ m∠BAC = 180° - 78°

⇒ m∠BAC = 102°

Learn more about isosceles trapezoids here:

https://brainly.com/question/23677333

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