Question #299930

If m<SDN=5x-2 and m<DNA=3x+4.


a. Find m<SDN


b. Find m<DSA



1
Expert's answer
2022-02-21T16:55:46-0500

If angles <𝟏 𝐚𝐧𝐝 <𝟐 are corresponding, or alternate interior, or alternate exterior, then they are equal, hence their measures are equal


thus;

𝟑𝒙+𝟒=𝟓𝒙𝟐𝟑𝒙 + 𝟒 = 𝟓𝒙 − 𝟐

𝟐𝒙=𝟔𝟐𝒙 = 𝟔

𝒙=𝟑𝒙 = 𝟑


If angles ⦟𝟏 𝐚𝐧𝐝 ⦟𝟐 are consecutive interior angles, then they add up to 𝟏𝟖𝟎° , hence

3𝒙+𝟒+𝟓𝒙𝟐=𝟏𝟖𝟎3𝒙 + 𝟒 + 𝟓𝒙 − 𝟐 = 𝟏𝟖𝟎

𝟖𝒙+𝟐=𝟏𝟖𝟎𝟖𝒙 + 𝟐 = 𝟏𝟖𝟎

𝟖𝒙=𝟏𝟕𝟖𝟖𝒙 = 𝟏𝟕𝟖

𝒙=113°𝟏𝟓.𝒙 = 113°𝟏𝟓' .

a)

m<SDN = 5x+25x+2

m<SDN = 5×22.25+25 \times 22.25 +2

m<SDN = 𝟐𝟐°𝟏𝟓'

b)

m<DSA = 3x+43x+4

m<DSA = 3×22.25+43\times22.25 + 4

m<DSA = 70°4𝟓


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