Question

what type of angle does ∠fdc form?
a) straight angle
b) right angle
c) obtuse angle
d) acute angle

Explanation:

Step1: Recall angle definitions

- Straight angle: \(180^\circ\), forms a straight line.
- Right angle: \(90^\circ\), forms a square corner.
- Obtuse angle: Greater than \(90^\circ\) but less than \(180^\circ\).
- Acute angle: Less than \(90^\circ\).

Step2: Analyze \(\angle FDC\)

From the diagram, \(\angle FDC\) is formed by lines \(FD\) and \(DC\). Visually, it appears to be less than \(90^\circ\) (acute) or? Wait, no—wait, let's check the lines. Wait, \(BE\) is vertical, and \(FC\) (or \(FD - DC\))—wait, actually, looking at the diagram, \(\angle FDC\): let's see the positions. Wait, maybe I misread. Wait, no—wait, the angle between \(FD\) and \(DC\): if we look at the intersection, \(BE\) is vertical, and the other line (with \(A, D, C\) and \(F, D, C\))—wait, actually, \(\angle FDC\): let's think about the angle measure. Wait, no, maybe the diagram shows that \(\angle FDC\) is acute? Wait, no, wait—wait, maybe I made a mistake. Wait, no, let's re-express:

Wait, the options: acute is less than \(90^\circ\), obtuse more than \(90^\circ\), right is \(90^\circ\), straight is \(180^\circ\). From the diagram, \(\angle FDC\) is formed by two lines intersecting, and the angle between \(FD\) and \(DC\) looks like it's less than \(90^\circ\)? Wait, no, wait—wait, maybe the correct answer is D? Wait, no, wait—wait, maybe I messed up. Wait, let's check again.

Wait, the diagram: points \(F, D, C\) are on a line? No, \(F\) is on one line, \(C\) on another, intersecting at \(D\) with \(BE\) vertical. Wait, \(\angle FDC\): the angle between \(FD\) and \(DC\). If we consider the lines, \(FD\) and \(DC\) form an angle. Let's see the other lines: \(AD\) and \(BE\) (vertical) – maybe \(AD\) is perpendicular to \(BE\)? Wait, if \(AD\) is perpendicular to \(BE\), then \(BE\) is vertical, \(AD\) is horizontal? No, \(AD\) is a slant. Wait, maybe the angle \(\angle FDC\) is acute. Wait, but let's think again.

Wait, the options: A is straight (180), B is right (90), C is obtuse (>90), D is acute (<90). From the diagram, \(\angle FDC\) is formed by two lines that are not perpendicular, not straight, and the angle looks small, so acute. Wait, but maybe I'm wrong. Wait, no—wait, maybe the correct answer is D? Wait, no, wait—wait, let's check the diagram again. The line with \(F\) and \(C\) is a straight line? No, \(F\) and \(C\) are on opposite sides of \(D\), so \(FDC\) is a straight line? No, \(F\) is on one ray, \(C\) on another. Wait, no, the angle at \(D\) between \(F\) and \(C\): if \(F\) and \(C\) are on a straight line, then it's a straight angle, but that's not the case. Wait, no, the diagram shows \(F\) on a line going down-left, \(C\) on a line going up-right, intersecting at \(D\) with \(B\) up, \(E\) down. So \(\angle FDC\) is the angle between \(FD\) (down-left) and \(DC\) (up-right). That angle is actually a straight angle? No, wait, no—wait, \(F\), \(D\), \(C\): are they colinear? If \(F\) and \(C\) are on a straight line through \(D\), then \(\angle FDC\) is a straight angle (180°), but that would be option A. Wait, maybe I misread the diagram. Let me re-express: the lines are \(FC\) (with \(F\) and \(C\)) and \(BE\) (with \(B\) and \(E\)) intersecting at \(D\), and \(A\) is on another line through \(D\). So \(\angle FDC\): if \(F\), \(D\), \(C\) are colinear, then it's a straight angle. Wait, that makes sense. So \(F\), \(D\), \(C\) are on a straight line, so \(\angle FDC\) is a straight angle (180°), so option A. Wait, but that contradicts my earlier thought. Let's check the definitions again. A straight angle is formed when two rays are opposite each other, forming a straight line, measure \(180^\circ\). So if \(F\), \(D\), \(C\) are colinear (on a straight line), then \(\angle FDC\) is a straight angle. So the correct answer is A.

Wait, maybe I made a mistake earlier. Let's confirm: a straight angle is \(180^\circ\), formed by two rays in a straight line. So if \(F\), \(D\), \(C\) are on a straight line, then \(\angle FDC\) is a straight angle. So the answer is A.

Answer:

A) Straight angle