answer this question---Chart/Diagram Description:
* **Type:** Geometric figure.
* **Main Elements:**
* **Points:** S, Q, R, T, P, H, G are labeled.
* **Lines/Segments:** Lines are drawn connecting S to T, T to Q, Q to P, S to Q, Q to R, S to R (collinear points S, Q, R), S to H, and a line segment starting at Q passing through G with an arrowhead indicating a direction.
* **Angles:**
* A right angle (90°) is marked at point Q, formed by the line TQP and the line SQR. This indicates ∠TQS = 90° and ∠TQR = 90°. Since TQP is a straight line, ∠SQP = 90° and ∠RQP = 90°.
* An angle labeled 60° is located at vertex P, within triangle QRP or TQP, likely ∠QPT = 60°.
* An angle labeled 30° is located at vertex R, within triangle RQT, likely ∠QRT = 30°.
* **Markings:**
* A single tick mark is present on line segment ST and line segment TQ, indicating that ST = TQ.
* A right angle symbol is shown at Q between TQ and SQR.
* An arrowhead is shown on the line extending from Q through G.
* **Relative Position and Direction:** Points S, Q, R appear collinear in a horizontal line from left to right. Point T is above and to the left of Q. Point P is below Q. Point H is on the line segment TQ. Point G is on the line segment QR. The line passing through Q and G extends away from Q in a direction roughly towards the bottom right.
Here is the extracted content from the image:
**Left Column Descriptions:**
* two obtuse vertical angles
* a pair of complementary nonadjacent angles
* an angle supplementary to $\angle$ HTS
* two acute vertical angles
* a linear pair whose vertex is G
* a pair of complementary adjacent angles
**Right Column (Options/Selected Answers):**
For "two obtuse vertical angles":
[Dropdown Menu Options (visible)]:
* $\angle$ QHG
* $\angle$ QGH and $\angle$ QGR
* $\angle$ QHG and $\angle$ PHT (Checked option)
* $\angle$ RQG and $\angle$ GQH
* $\angle$ QRG and $\angle$ TPH
* $\angle$ RQG and $\angle$ QHG
* $\angle$ PTH
* $\angle$ QHT and $\angle$ PHG
For "a pair of complementary nonadjacent angles":
[Choose] (Dropdown is closed)
For "an angle supplementary to $\angle$ HTS":
$\angle$ QRG and $\angle$ TPH (Selected option in closed dropdown)
For "two acute vertical angles":
$\angle$ QHT and $\angle$ PHG (Selected option in closed dropdown)
For "a linear pair whose vertex is G":
[Choose] (Dropdown is closed)
For "a pair of complementary adjacent angles":
[Choose] (Dropdown is closed)
视频信息
答案文本
视频字幕
We have a geometric figure with points S, Q, R collinear on a horizontal line. Point T is above and to the left of Q, while point P is directly below Q. There's a right angle at Q between line TQ and line SQR. We can see angle markings of 60 degrees at P and 30 degrees at R. Equal tick marks show that ST equals TQ. Our task is to identify various angle relationships in this configuration.
At point H, we can see two pairs of vertical angles. The obtuse vertical angles are angle QHG and angle PHT, which are opposite each other when lines intersect at H. The acute vertical angles are angle QHT and angle PHG. These pairs demonstrate the fundamental property that vertical angles are always equal to each other.
Now let's examine complementary and supplementary angle relationships. At point R, we can see a 30-degree angle. Its complement would be 60 degrees, since 30 plus 60 equals 90 degrees. For supplementary angles, we look at angle HTS which measures 60 degrees. An angle supplementary to this would measure 120 degrees, since 60 plus 120 equals 180 degrees.
Linear pairs are formed when two adjacent angles create a straight line, making their sum equal to 180 degrees. At point G, we can identify a linear pair where two angles are adjacent and supplementary. We also have complementary adjacent angles at point Q, where two angles share a vertex and a common side, and their measures add up to 90 degrees.
In summary, we have successfully identified all the angle relationships in this geometric figure. The obtuse vertical angles are angle QHG and angle PHT. The acute vertical angles are angle QHT and angle PHG. We found complementary angles with measures of 30 degrees and 60 degrees. For supplementary relationships, we identified angles that sum to 180 degrees. These fundamental angle relationships are essential tools in geometric analysis and problem solving.