Question

Complete the statements to find the measurements of ∠a and ∠b .

Answer 1

∠a = 80° and ∠b = 50°

Explanation:

Look at angle a. Angle a and 100 both lie on the same line, which means they are supplementary and add up to 180. Then we can write: m∠a + 100 = 180. To solve this for a, we simply subtract 100 from both sides:

m∠a = 80°

Now, look at the triangle. All the angles in a triangle add up to 180, so we have the equation: m∠b + 80 + 50 = 180. Solve for b by subtracting 80 and 50 from both sides: m∠b = 50°.

Thus, ∠a = 80° and ∠b = 50°.

Answer 2

∠a=80

∠b=50

Explanation:

∠a and 100 are on a straight line. Therefore they are supplementary, and add to 180 degrees. So, we can say that:

∠a+100=180

To solve, subtract 100 from both sides. This will leave ∠a by itself.

∠a +100-100=180-100

∠a=80

The angles in a triangle must add to 180 degrees. Therefore,

∠a + ∠b + 50= 180

We know ∠a is 80, so we can substitute that in

80+ ∠b +50 =180

∠b+80+50=180

Combine like terms

∠b+(80+50)=180

∠b+130=180

To solve, subtract 130 from both sides. This will leave ∠b by itself.

∠b+130-130=180-130

∠b=50