Question

Find the value of x by filling the blanks in the provided statement-reason solutions

Answer 1

Answer:

1]$measure\ angle\ DCA=measure\ angle\ CAB=18\ degree$

2]$measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree$

3]$18\ degree+3x+3x=180\ degree$

4]$x=27$

Step-by-step explanation:

Given:-measure angle DCA = 18 degree

line AB II line DC

Solution:-

1] measure angle DCA and measure angle CAB are interior  alternate angles and interior alternate angles are equal.

$measure\ angle\ DCA=measure\ angle\ CAB=18\ degree$------------------ (Equation 1)

Therefore the equation for statement number 1 is $measure\ angle\ DCA=measure\ angle\ CAB=18\ degree$

2]Sum of interior angles of triangle is equal to 180 degree.

In Triangle ABC,

measure angle A+measure angle B+measure angle C=180 degree

Therefore the equation for statement number 2 is measure angle A+measure angle B+measure angle C=180 degree

3] In Triangle ABC,

$measure\ angle\ B=3x---------------(Given)$

$measure\ angle\ C=3x---------------(Given)$

$measure\ angle\ A=18\ degree---------------(from\ equation\ [tex]measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree$

Now substituting the value of angles we get,

$18\ degree+3x+3x=180\ degree-------------(Equation\ 2)$

Therefore the equation for statement number $3\ is\ 18\ degree+3x+3x=180\ degree$

4] After solving the equation 2 we get,

$18+3x+3x=180$

$6x=180-18$

$6x=162$

$x=27\ degree$

Therefore value of $x=27\ degree$