Question

Big Avenue and Pecan Road make a 130° angle. The angle of Pecan Road and Main Street is 20°. What kind of triangle do the three streets form?
obtuse triangle
acute triangle
right triangle
equilateral triangle

Answer 1

To determine the type of triangle formed by the three streets, we first need to find the measure of the third angle.

1. We know that the angle between Big Avenue and Pecan Road is 130°.
2. The angle between Pecan Road and Main Street is 20°.

To find the measure of the third angle (angle between Main Street and Big Avenue), we can use the property that the sum of all angles in a triangle is 180°.

Let's denote the angles as follows:
- Angle A (Big Avenue and Pecan Road) = 130°
- Angle B (Pecan Road and Main Street) = 20°
- Angle C (Main Street and Big Avenue) = ?

We can find Angle C using the formula:
\[
Angle C = 180° - (Angle A + Angle B)
\]
\[
Angle C = 180° - (130° + 20°)
\]
\[
Angle C = 180° - 150°
\]
\[
Angle C = 30°
\]

Now we have all three angles:
- Angle A = 130°
- Angle B = 20°
- Angle C = 30°

To classify the triangle:
- An obtuse triangle has one angle that is greater than 90°.
- An acute triangle has all angles less than 90°.
- A right triangle has one angle equal to 90°.
- An equilateral triangle has all angles equal to 60°.

Since one of the angles (130°) is greater than 90°, the triangle formed by Big Avenue, Pecan Road, and Main Street is classified as an **obtuse triangle**.