Question

find the measure of the missing angles.
answer attempt 2 out of 2
d = 70 °
e = 87 °
f = °

Explanation:

Step1: Identify straight angle

A straight angle is \(180^\circ\). For angle \(f\), we can use the sum of angles on a straight line. The angles \(87^\circ\), \(d = 70^\circ\), and \(f\) should sum to \(180^\circ\)? Wait, no, actually, looking at the vertical and horizontal lines, the angle adjacent to \(87^\circ\) and the angle with \(70^\circ\) – wait, actually, the angle \(f\) is vertical to the \(87^\circ\)? No, wait, let's see: the horizontal line and the line with \(87^\circ\) and \(d\) (which is \(70^\circ\)) – wait, no, the angle \(f\) is equal to the angle opposite to the \(87^\circ\)? Wait, no, let's calculate the sum of angles around a point or on a straight line. Wait, the angle between the horizontal line and the line with \(87^\circ\) and \(d\) (70°) – actually, the angle \(f\) can be found by knowing that the sum of angles on a straight line is \(180^\circ\). Wait, the angle with \(87^\circ\), \(d = 70^\circ\), and \(f\) – wait, no, the horizontal line: the angle \(87^\circ\), \(d = 70^\circ\), and then the angle \(f\) and the other angle. Wait, actually, the angle \(f\) is equal to the angle that is \(180^\circ - 87^\circ - 70^\circ\)? Wait, no, let's look at the vertical lines. Wait, the angle \(e\) is \(87^\circ\), \(d\) is \(70^\circ\), and then the angle \(f\) – wait, the angle between the two lines (the one with \(70^\circ\) and the horizontal line) and the other line. Wait, actually, the angle \(f\) is equal to \(180^\circ - 87^\circ - 70^\circ = 23^\circ\)? Wait, no, wait, the sum of angles on a straight line: the horizontal line has angles \(87^\circ\), \(d = 70^\circ\), and \(f\) – no, wait, the vertical line: the angle \(e\) is \(87^\circ\), \(d\) is \(70^\circ\), and then the angle between the two lines (the one with \(70^\circ\) and the vertical line) is \(70^\circ\), and the angle \(e\) is \(87^\circ\). Wait, maybe the angle \(f\) is equal to \(180^\circ - 87^\circ - 70^\circ = 23^\circ\)? Wait, no, let's check: the sum of angles around point \(e\) (the intersection) should be \(360^\circ\), but for straight lines, adjacent angles sum to \(180^\circ\). Wait, the angle \(f\) is vertical to the angle that is \(87^\circ\)? No, wait, the angle \(f\) is equal to the angle opposite to the \(87^\circ\)? No, wait, the angle between the horizontal line and the line with \(f\) is equal to the angle between the horizontal line and the line with \(87^\circ\)? No, wait, the angle \(f\) is equal to \(180^\circ - 87^\circ - 70^\circ = 23^\circ\)? Wait, let's calculate: \(87 + 70 + f = 180\) (since they are on a straight line). So \(f = 180 - 87 - 70 = 23\). Wait, that makes sense. So \(f = 23^\circ\).

Step1: Sum of angles on a straight line

Angles on a straight line sum to \(180^\circ\). So \(87^\circ + 70^\circ + f = 180^\circ\).

Step2: Solve for \(f\)

\(f = 180 - 87 - 70 = 23\).

Answer:

\(f = \boxed{23}\)