Get the answer to "Find the valve of?"

High School
Geometry
High school geometry
Circles

Sabrina Waller

Answered question

2022-02-12

Find the valve of?

Answer & Explanation

iluvyou234521ip

Beginner2022-02-13Added 12 answers

Step 1
Consider two chords to the circle intersect at a point inside the circle as shown in the figure.

According to the property of circles, the measure of angle x is calculated as,

x = \frac{1}{2} (\hat{A B} + \hat{C D})

Step 2
Use the property of angles
Consider the given circle. The intersection of chords intercepts two arcs UM and ST.
Now, according to the property of circles,

91^{\circ} = \frac{1}{2} (\hat{U M} + \hat{S T})

Now, let the unknown angle be denoted by x.
Thus,

91^{\circ} = \frac{1}{2} (57^{\circ} + x)

Now, solve the obtained equation for x.

182^{\circ} = 57^{\circ} + x

x = 125^{\circ}

Thus, the measure of unknown angle is obtained as 125 degrees.

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