Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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 ∘

Sagot :

⟨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

#SPJ1

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.