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In the following diagram, {HI}


start overline, H, I, end overline is parallel to {JK}


start overline, J, K, end overline.

What is the measure of

Angles are not necessarily drawn to scale.

In the following diagram HI start overline H I end overline is parallel to JK start overline J K end overlineWhat is the measure ofAngles are not necessarily dr class=

Respuesta :

Sum of interiors =exterior angle

[tex]\\ \sf\longmapsto <I=56+66[/tex]

  • Add both

[tex]\\ \sf\longmapsto <I=122[/tex]

Now

[tex]\\ \sf\longmapsto I+x=180[/tex]

[tex]\\ \sf\longmapsto x+122=180[/tex]

[tex]\\ \sf\longmapsto x=180-122[/tex]

[tex]\\ \sf\longmapsto x=58[/tex]

The measure of x° is 58° .

What are corresponding angles?

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

What is corresponding angles theorem?

According to the corresponding angles theorem, the statement “If a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent”  

According to the question

In the triangle AHI  

∠A = 66°

∠H = 56°

By using sum of angle of triangle = 180°  

∠A + ∠H + ∠I  = 180°  

66° + 56° + ∠I  = 180°

∠I  = 180° - 122°

∠I  = 58°

As , given HI is parallel to JK

Now,

According to the corresponding angles theorem

If a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent .

Therefore,

∠I  = ∠K = x°  

i.e

x° = 58°

Hence, the measure of x° is 58° .

To know more about corresponding angles theorem here:

https://brainly.com/question/16987080

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