Answer:
38 degrees.
Step-by-step explanation:
There are 180 degrees in a triangle, so
m<1 = 180 - (43 + 74)
= 180 - 117
= 63 degrees.
m < 2 = m < 1 ( opposite angles) so
m < 2 = 63 degrees.
Finally, m < 3 = 180 - (63 + 79)
== 180 - 142
= 38 degrees.
For given figure, the measure of angle 3 is 38°.
"These angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent."
For given example,
Consider left half part of the figure, which is a triangle.
We know, the sum of all angles of the triangle is 180°.
⇒ 43° + 74° + ∠1 = 180°
⇒ 117° + ∠1 = 180°
⇒ angle 1 = 63°
From the figure, we can observe that the angles 1 and 2 are opposite angles.
This means angle 1 and angle 2 are congruent.
⇒ angle 2 = 63°
Now, consider the right half part of the figure, which is a triangle.
⇒ 79° + ∠2 + ∠1 = 180°
⇒ 79° + 63° +∠1 = 180°
⇒ angle 1 = 38°
Therefore, the measure of angle 3 is 38°.
Learn more about opposite angles here:
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