The size of angle x is 99 degree
What is straight angle and Exterior angle theorem?
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. straight angle: an angle whose sides lie in opposite directions from the vertex in the same straight line and which equals two right angles.
We have,
∠CDE = [tex]123^{o}[/tex]
∠BCD = [tex]42^{o}[/tex]
∠ABC = [tex]x^{o}[/tex]
According to the question
Angle Addition Postulate and definition of straight angle:
∠BDC+∠CDE = [tex]180^{O}[/tex]
Substitute into : ∠BDC + [tex]123^{o}[/tex] = [tex]180^{o}[/tex]∠BDC = [tex]180^{o}[/tex] - [tex]123^{o}[/tex]∠BDC = [tex]57^{o}[/tex]
Exterior Angle Theorem:
∠BDC + ∠BCD = ∠ABC
Substitute into :
[tex]57^{o}[/tex] + [tex]42^{o}[/tex]
= [tex]x^{o}[/tex][tex]x^{o}[/tex]
= [tex]99^{o}[/tex]
hence, the size of angle x is 99 degree
Learn more about exterior angle theorem from here
https://brainly.com/question/956912
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