Complete the statements to find the measurements of ∠a
and ∠b
.
A triangle with angles labeled a, b, and 50 degrees. A line extends from angle a to form exterior angle with measure 100 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=
°
m ∠a + 100° = 180°
m ∠a = 80°
b = 180° - a - 50°
b = 180° - 80° - 50°
b = 50°
Two angles are complementary.
One of the angles has a measure of 20°
.
What is the measure of the other angle?
A ray extends from an angle to create 2 angles. 1 angle has measure 20 degrees and the second angle has measure question mark.
CLEAR CHECK
70°
20°
160°
110°
The measure of the other angle is 70°.
Explanation:
Complementary angles add up to 90°. Since one angle has a measure of 20°, its complement must have a measure of 90° - 20° = 70°.
To find the measurement of ∠a, we know that the angle formed by the line extending from ∠a to form an exterior angle is given as 100 degrees. Since the sum of the interior and exterior angles formed at a vertex is always 180 degrees, we can subtract 100 degrees from 180 degrees to find ∠a.
So,
m ∠a + 100° = 180°
Subtracting 100° from both sides:
m ∠a = 80°
Therefore, the measurement of ∠a is 80 degrees.
To find the measurement of ∠b, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees. So, if we subtract the known angles (∠a and the given angle of 50 degrees) from 180 degrees, we can find ∠b.
m ∠b + ∠a + 50° = 180°
Substituting the value of ∠a (80°):
m ∠b + 80° + 50° = 180°
Combine like terms:
m ∠b + 130° = 180°
Subtracting 130° from both sides:
m ∠b = 50°
Therefore, the measurement of ∠b is 50 degrees.