Question

If m angle BDC = 3(x-5) and m Arc BC = x+25 what is m angle A?

Answer 1

Step-by-step explanation:

If m angle BDC = 3(x-5) =3x-15

m Arc BC = x+25

m angle A=3x-15×x+25

3x-x×+25+15

Answer=2x×40

Answer 2

Answer:

The angle A is $\frac{1}{2} x$, where x is the measure of arc BC minus 25.

Step-by-step explanation:

The knowledge that the measure of an angle created by two intersecting chords equals half the sum of the measures of the arcs the angle intercepts must be used to solve this problem.

Let's begin by determining the length of arc BD. Since arc BD is a semicircle (which has measure 180 degrees) and arc BC has measure x + 25, arc BD must have measure x.

180 - (x + 25) = 155 - x.

Now, we may use the aforementioned knowledge to determine the size of the BDC angle.

We know that angle BDC is formed by the chords BD and DC, and it intercepts arcs BD and BC.

Therefore, we have:

m angle BDC =$\frac{1}{2}$ (m arc BD + m arc BC)

= $\frac{1}{2} \times$ [(155 - x) + (x + 25)]

= 90 - $\frac{1}{2}x$

Finally, we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle A. We have:

m angle A = 180 - m angle BDC - m angle BCD

= 180 - (90 - $\frac{1}{2} x$) - 90

$= \frac{1}{2} x$

Therefore, the measure of angle A is $\frac{1}{2} x$, where x is the measure of arc BC minus 25.

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