Answer:
∠3 = 102°
Step-by-step explanation:
║A straight line always equals 180°. So all we need to do is subtract 78° ║from 180° for the missing angle.
180 − 78 = 102
∠3 = 102°
Further explanation:
║The image shows two slanted lines across one vertical line. If we visualize ║a <em>circle</em> around the point where the slanted line intercepts with the vertical ║line, we can solve this.
<em>[we only need one line to work with, because both lines are parallel]</em>
║That circle you visualized divides the intercept into <em>four sectors</em>. One of ║those sectors, or angles, is labled 78°. We need to find the angle measure ║underneath the labled sector. The sector in the bottom right corner has ║the same angle measure as the labled sector, which is 78°. The sector ║labled ∠3 has the same angle measure as the sector in the upper right.
<em>[a full rotation around an angle is always 360°]</em>
║This can be easily solved by subtracting 78° from 180° to get the angle ║measure for the upper right sector, which is equivalent to ∠3. Using basic ║subtraction, 180° − 78° = 102°. We can prove this by multiplying 78° by 2, ║multiplying 102° by two, and adding the products.
78 ⋅ 2 = 156
102 ⋅ 2 = 204
204 + 156 = 360
║Because the sums equal 360°, we can determine the answer is true.
