Question

Using the picture above, and given that y= 24,z = 5 and p = 10, find the length of segment x.
(1 point)
12
22
29
48

Lines SQ and SU are secants. If
, find x.
(1 point)
= 12, = SR 30, = 9 and = 5x − 24 ¯¯¯¯¯¯¯ SQ ¯¯¯¯¯¯¯ ST ¯¯¯¯¯¯¯ TU ¯¯¯¯¯¯¯
360
11
40
31

If
then what is the length of AO to the nearest whole inch?
(1 point)
= BO 45 in and = 108 in ¯¯¯¯¯¯¯¯ BA ¯¯¯¯¯¯¯¯
AO =

If arc JK is 5x - 59 and angle JMK is 4x - 32, find the measure of angle JLK
(1 point)
27 degrees
152 degrees
76 degrees
38 degrees

If arc KJ = 13x - 10 and arc JI = 7x - 10, then find the m<KIJ
(1 point)
10 degrees
120 degrees
80 degrees
60 degrees

XZ is a diameter. The measure of the angel at X is 59 degrees. What is the measure of arc XY?

Answer 1

I can solve the ones that have enough information from the text, but I’m missing the pictures/diagrams needed for the first three problems. Please upload the image or describe the diagram for those. From the text problems I can solve:

- If arc JK = 5x − 59 and ∠JMK = 4x − 32, and M is the center, then 4x − 32 = 5x − 59 ⇒ x = 27. Arc JK = 5(27) − 59 = 76°, so any inscribed angle intercepting that arc (such as ∠JLK) = 1/2·76° = 38°. Answer: 38°.

- If arc KJ = 13x − 10 and arc JI = 7x − 10, taking x = 10 makes arc KJ = 120° and arc JI = 60° (and the remaining arc KI = 180°). Then ∠KIJ is an inscribed angle intercepting arc KJ, so ∠KIJ = 1/2·120° = 60°. Answer: 60°.

- XZ is a diameter. An inscribed angle at X intercepts arc YZ, so m(arc YZ) = 2·∠X = 2·59° = 118°. Since arc XZ is 180° (a semicircle), arc XY = arc XZ − arc YZ = 180° − 118° = 62°. Answer: 62°.

For the other three (the x from the first picture, the secant equation with SQ and SU, and the AO length problem) I need the corresponding diagram or a clearer statement (which segments are whole secants versus external parts, and whether BA is an arc length or a chord, etc.). Send the image or clarify those details and I’ll finish them.