Answer to Question #299930 in Geometry for Lawincie Buduan

Question

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

a. Find m<SDN

b. Find m<DSA

Answer 1

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

thus;

$𝟑𝒙 + 𝟒 = 𝟓𝒙 − 𝟐$

$𝟐𝒙 = 𝟔$

$𝒙 = 𝟑$

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

$3𝒙 + 𝟒 + 𝟓𝒙 − 𝟐 = 𝟏𝟖𝟎$

$𝟖𝒙 + 𝟐 = 𝟏𝟖𝟎$

$𝟖𝒙 = 𝟏𝟕𝟖$

$𝒙 = 113°𝟏𝟓' .$

a)

m<SDN = $5x+2$

m<SDN = $5 \times 22.25 +2$

m<SDN = 𝟐𝟐°𝟏𝟓'

b)

m<DSA = $3x+4$

m<DSA = $3\times22.25 + 4$

m<DSA = 70°4𝟓