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Find the value of x in each case. Please put statement reasons.

Find the value of x in each case. Please put statement reasons.-example-1
User Mayur Patel
by
2.5k points

1 Answer

17 votes
17 votes

Answer:

x = 10°

Explanation:

Given the figure with angles 2x, 4x, 5x, and 50° marked, you want to find the value of x.

Development

∠HAC = ∠HCA . . . . base angles of isosceles triangle HAC

2(∠HAC) = 4x . . . . . exterior angle 4x is equal to the sum of the equal remote interior angles HAC and HCA

∠HAC = 2x . . . . . . . divide by 2

∠AED = 180° -2x -2x = 180° -4x . . . . sum of angles in ∆AED is 180°

∠AHC = 180° -4x . . . . angles at H are a linear pair

HC ║ ED . . . . converse of corresponding angles theorem

∠FEG = ∠FCH = 50° . . . . . corresponding angles theorem

5x = 50° . . . . . substitute value of ∠FEG

x = 10° . . . . . divide by 5

Using this value for the marked angles, we get the measures shown in the attachment.

Find the value of x in each case. Please put statement reasons.-example-1
User Lugaru
by
2.8k points
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