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The angle measurements in the diagram are represented by the following expressions. \qquad \blueD{\angle A=7x + 40^\circ}∠A=7x+40 ∘ start color #11accd, angle, A, equals, 7, x, plus, 40, degrees, end color #11accd \qquad\greenD{\angle B=3x + 112^\circ}∠B=3x+112 ∘ start color #1fab54, angle, B, equals, 3, x, plus, 112, degrees, end color #1fab54 Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd: \blueD{\angle A} =∠A=start color #11accd, angle, A, end color #11accd, equals ^\circ ∘

Answer :

⟨A = 7•x + 40° and ⟨B = 3•x + 112°

From a possible diagram of the question, ⟨A = ⟨B, which gives;

  • x = 18°
  • ⟨A = 166°

How can the value of x and the measure of ⟨A be found?

Given;

⟨A = 7•x + 40°

⟨B = 3•x + 112°

In the diagram from a similar question posted online, we have;

  • ⟨A and ⟨B are corresponding angles

Corresponding angles formed by parallel lines having a common transversal are congruent, therefore;

  • ⟨A and ⟨B are congruent

Which gives;

  • ⟨A = ⟨B

7•x + 40° = 3•x + 112°

7•x - 3•x = 112° - 40° = 72°

7•x - 3•x = 4•x = 72°

x = 72° ÷ 4 = 18°

Therefore;

  • x = 18°

Which gives;

⟨A = 7•x + 40°

⟨A = 7 × 18 + 40° = 166°

  • The measure of angle ⟨A = 166°

Learn more about angles formed by parallel lines that have a common transversal here:

https://brainly.com/question/13209798

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