The measure of angle 4 is 120°, and the measure of angle 2 is 35°.
Triangle A B C. Angle A is 2, angle B is 1, angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.
What is the measure of angle 5?
95°
105°
130°
155°
ON A TIMEDDD QUIZZZ
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interior angle C is 180-120 = 60
A+C = 95, so B = 85
exterior at B is 180-85 = 95
To find the measure of angle 5, we need to use the property of exterior angles of a triangle, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
From the given information, we know that the exterior angle to angle B is 5. Therefore, angle 5 is the sum of angles 1 and 5 (the remote interior angles to angle 5). Similarly, the exterior angle to angle C is 4, so angle 4 is the sum of angles 3 and 4 (the remote interior angles to angle 4).
Now, let's find the measures of angles 1 and 3:
Given:
Angle 2 = 35°
Triangle ABC:
Angle A = 2
Angle B = 1
Angle C = 3
Using the property that angles of a triangle add up to 180°, we have:
Angle A + Angle B + Angle C = 180°
2 + 1 + 3 = 180°
6 = 180°
Therefore, each angle in Triangle ABC has a measure of 30°, since 180° divided by 6 is 30°.
Now, we can find the measures of angles 1 and 3:
Angle 1 = 30° (as mentioned above)
Angle 3 = 30° (as mentioned above)
Since angle 4 is given as 120°, we can find the measure of angle 5:
Angle 4 = Angle 3 + Angle 4
120° = 30° + Angle 3
Angle 3 = 120° - 30°
Angle 3 = 90°
Now, using the property of exterior angles, we know that:
Angle 5 = Angle 1 + Angle 5
Angle 5 = 30° + Angle 1
Angle 5 = 30° + 90°
Angle 5 = 120°
Therefore, the measure of angle 5 is 120°.
So, the correct answer is 120°.