Question

Use quadrilateral ABCD to find the value of x. The figure is not drawn to scale. Use the following dimensions: m⦨ABC = 4x◦, m⦨BCD = 3x◦, m⦨CDA = 2x◦, m⦨DAB = 3x◦. Use the formula, (n – 2)180 to find the total degrees of the polygon. Write an equation and solve for x. You found the measures of the 4 interior angles in Question 2. Now, explain in 2-3 sentences how you can use them⦨CDA to find the measure of exterior angle ⦨ADE. Find them⦨ADE

Answer 1

Answer/Step-by-step explanation:

1. Given:

m<ABC = 4x°,

m<BCD = 3x°,

m<CDA = 2x°,

m<DAB = 3x°

Sum of quadrilateral = (n - 2)180

Quadrilateral has 4 sides, therefore, n = 4.

Sum of quadrilateral = (4 - 2)180 = 2*180 = 360°

Equation to solve for x would be:

m<ABC + m<BCD + m<CDA + m<DAB = 360

Substituting the given expression for each angle, we have:

4x + 3x + 2x + 3x = 360

12x = 360

Use the above equation to solve for x by dividing both sides by 12

x = 30

Find the measures of all the interior angles by substituting the value of x in each given expression for each angle as follows:

m<ABC = 4x = 4*30 = 120°

m<BCD = 3x = 3*30 = 90°

m<CDA = 2x = 2*30 = 60°

m<DAB = 3x = 3*30 = 90°

[Check: 120 + 90 + 60 + 90 = 360°]

2. <CDA and <ADE form a linear pair. They are supplementary angles.

Since supplementary angles sum up to equal 180°, and <ADE is a supplement of <CDA (60°), therefore:

m<ADE = 180° - 60° = 120°