Answer:
x° = 37°
Step-by-step explanation:
* Lets revise some facts of a circle
- The secant is a line intersect the circle in two points
- If two secants intersect each other in a point outside the circle,
then the measure of the angle between them is half the difference
of the measures of their intercepted arcs
* Now lets solve the problem
- There is a circle
- Two secants of this circle intersect each other in a point outside
the circle
∴ The measure of the angle between them = 1/2 the difference of the
measures of their intercepted arcs
∵ The measure of the angle between them is x°
∵ The measures of their intercepted arcs are 26° and 100°
- Use the rule above to find x
∴ x° = 1/2 [ measure of the large arc - measure of small arc]
∵ The measure of the large arc is 100°
∵ The measure of the small arc is 26°
∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°
∴ x° = 37°
Answer:
x = 21
Step-by-step explanation:
You can solve this problem by using similar triangles. You can tell that the two triangles are similar by AAA (since two angles are the same, the third must be too).
Now that we've established that the triangles are similar, you need to identify the corresponding sides:
12 corresponds to 28
9 corresponds to x
In order to find x, you'll need to find the scale factor, which you can find by dividing 28 by 12:
28 ÷ 12 = 7/3
Now that you know that 7/3 is the scale factor, you can multiply it by 9 to find x:
9 × 7/3 = x
x = 63/3
x = 21
(Top left) 1. 5 1/24
(Bottom left)2. 11 1/3
(Top right)3. 8 13/14
(Bottom Right)4. 20 29/35
