In the given question, the options are related to linear pair .
And according to linear pair, if a line cuts another line at a point, then the sum of the adjacent angles formed at that point is 180 degree.
Therefore, from the given diagram we can say that, angles WXY and YXZ are linear pair, so there sum have to be 180.
[tex]\angle WXY + \angle YXZ =180[/tex]
And the correct option is the third option .
The true statement regarding the diagram is [tex]\boxed{{\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{YXZ}} = {{180}^ \circ }}[/tex]. Option (c) is correct.
Further explanation:
Given:
The options are as follows,
(a). [tex]{\text{m}}\angle {\text{WXY}} = {\text{m}}\angle {\text{YXZ}}[/tex]
(b). [tex]{\text{m}}\angle {\text{WXY}} < {\text{m}}\angle {\text{YZX}}[/tex]
(c). [tex]{\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{YXZ}} = {180^\circ }[/tex]
(d). [tex]{\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{XYZ}} = {180^\circ }[/tex]
Explanation:
The sum of two angles that are on the same line and having common vertex is 180 degree.
The angles that are on the same line is known as linear pair. The sum of linear pair is 180 degree.
[tex]{\text{m}}\angle {\text{WXY and m}}\angle {\text{YXZ}}[/tex] are on the same line WZ with common vertex X. Therefore, the angles form a linear pair.
Hence, the sum of the angles is [tex]{180^ \circ }.[/tex]
The true statement regarding the diagram is [tex]\boxed{{\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{YXZ}} = {{180}^ \circ }}[/tex]. Option (c) is correct.
Option (a) is not correct.
Option (b) is not correct.
Option (c) is correct.
Option (d) is not correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Angles
Keywords: statements, diagram, true statement, parallel, linear pair, sum, adjacent angle, corresponding angles, 180 degree.
