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3 years ago

Which statement regarding the diagram is true? m∠WXY = m∠YXZ m∠WXY < m∠YZX m∠WXY + m∠YXZ = 180° m∠WXY + m∠XYZ = 180°

Mathematics

2 answers:

Degger [83]3 years ago

7 0

The true statement regarding the diagram is $\boxed{{\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{YXZ}} = {{180}^ \circ }}$ . Option (c) is correct.

Further explanation:

Given:

The options are as follows,

(a). ${\text{m}}\angle {\text{WXY}} = {\text{m}}\angle {\text{YXZ}}$

(b). ${\text{m}}\angle {\text{WXY}} < {\text{m}}\angle {\text{YZX}}$

(c). ${\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{YXZ}} = {180^\circ }$

(d). ${\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{XYZ}} = {180^\circ }$

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.

${\text{m}}\angle {\text{WXY and m}}\angle {\text{YXZ}}$ are on the same line WZ with common vertex X. Therefore, the angles form a linear pair.

Hence, the sum of the angles is ${180^ \circ }.$

The true statement regarding the diagram is $\boxed{{\text{m}}\angle {\text{WXY}} + {\text{m}}\angle {\text{YXZ}} = {{180}^ \circ }}$ . Option (c) is correct.

Option (a) is not correct.

Option (b) is not correct.

Option (c) is correct.

Option (d) is not correct.

Learn more:

Learn more about inverse of the function brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Angles

Keywords: statements, diagram, true statement, parallel, linear pair, sum, adjacent angle, corresponding angles, 180 degree.

elena55 [62]3 years ago

5 0

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.

$\angle WXY + \angle YXZ =180$

And the correct option is the third option .

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4. The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

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6. The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

Step-by-step explanation:

Lets revise some important rules

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The mid point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
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∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 7 and $x_{2}$ = 4

∵ $y_{1}$ = 2 and $y_{2}$ = 6

∴ $m=\frac{6-2}{4-7}=\frac{4}{-3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $\frac{3}{4}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{7+4}{2},\frac{2+6}{2})$

∴ The mid-point = $(\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)$

- Substitute the value of the slope in the form of the equation

∵ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = $\frac{3}{4}$ × $\frac{11}{2}$ + b

∴ 4 = $\frac{33}{8}$ + b

- Subtract $\frac{33}{8}$ from both sides

∴ $-\frac{1}{8}$ = b

∴ y = $\frac{3}{4}$ x - $\frac{1}{8}$

∴ The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

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- Use the formula of the slope to find its slope

∵ $x_{1}$ = 8 and $x_{2}$ = 4

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∴ The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

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