Question

NO LINKS!! URGENT HELP PLEASE!!


Find the value of x° for both circles please

Answer 1

`\textsf{1)} \quad x=96`

`\textsf{2)} \quad x=30`

Explanation:

To find the value of x for both circles, we can use the Angles of Intersecting Chords Theorem.

Angles of Intersecting Chords Theorem

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

`\hrulefill`

Question 1

The angle that is the supplement to angle x (forms a straight line with x) can be found using the Angles of Intersecting Chord Theorem.

`\begin{aligned}\textsf{Angle supplement to $x^(\circ)$}&=(1)/(2)(100^(\circ)+68^(\circ))\\\\&=(1)/(2)(168^(\circ))\\\\&=84^(\circ) \end{aligned}`

Supplementary angles sum to 180°. Therefore, to find the measure of angle x, subtract the supplementary angle from 180°:

`x^(\circ)=180^(\circ)-84^(\circ)`

`x^(\circ)=96^(\circ)`

`x=96`

Therefore, the value of x is 96.

`\hrulefill`

Question 2

According to the Angles of Intersecting Chord Theorem, the measure of the angle labelled 78° is half the sum of the measures of the intercepted arcs labelled x° and 126°. Therefore:

`\begin{aligned}78^(\circ)&=(1)/(2)(x^(\circ)+126^(\circ))\\\\ 2 \cdot 78^(\circ)&=2 \cdot (1)/(2)(x^(\circ)+126^(\circ))\\\\156^(\circ)&=x^(\circ)+126^(\circ)\\\\x^(\circ)&=156^(\circ)-126^(\circ)\\\\x^(\circ)&=30^(\circ)\\\\x&=30\end{aligned}`

Therefore, the value of x is 30.

Answer 2

x=96°
x=30°

Explanation:

We know that:
Angles between intersecting chords theorem: States that:

The Angles between Intersecting Chords Theorem states that the measure of an angle formed by two chords that intersect inside a circle is equal to the arithmetic mean of the measures of the two intercepted arcs.

By using this

For First:

`y=(100+68)/(2)= 84`

y=84°

Since x and y are in linear pair.

So,

x+y=180°

x=180°-y

x=180-84°

x=96°

For second:

`78=(x+126)/(2)`

doing criss cross multiplication:

x+126=78*2

x=156-126

x=30°