Complete the statements to find the measurements of ∠a

Question

and ∠b
.

A triangle with angle measures a, b, and 70 degrees. A line extends from angle a to form exterior angle 120 degrees.
CLEARCHECK
Find the measurement of ∠a
.

m∠a +
°
=180°

m∠a =

°
Find the measurement of ∠b
using the measures of the other two angles in the triangle.

m∠b +
°
+

°
=180°

m∠b =
°

Answer 1

m∠a + 120° = 180°

m∠a = 60°

m∠b + 70° + 120° = 180°

m∠b = 180° - 70° - 120°

m∠b = 10°

Answer 2

Find the measurement of ∠b
using the measures of the other two angles in the triangle.

m∠b +
°
+

°
=180°

m∠b =
°

Answer 3

In this case:

m∠b + 70° + 120° = 180°

m∠b = 180° - 70° - 120° = 180° - 190° = -10°

However, angles cannot have negative measurements, so it seems there was a mistake in the calculation. Let's correct it:

m∠b = 180° - 70° - 120°

m∠b = 180° - 190°

m∠b = -10°

Since angles in a triangle cannot have negative measurements, it seems the provided angle measures are not possible to form a valid triangle.

Answer 4

wrong from the get-go.
you should have started off with
m∠a + m∠b + 70° = 180°
as you said, m∠a = 60°, so that leaves
60° + m∠b + 70° = 180°
giving m∠b = 50°

Answer 5

You are correct, and I apologize for the mistake in my initial response. Thank you for providing the correct method and calculation.

m∠a + m∠b + 70° = 180°

60° + m∠b + 70° = 180°

m∠b + 130° = 180°

m∠b = 180° - 130°

m∠b = 50°

Therefore, ∠b = 50°. Thank you for the correction.