Question

Determine the measure of the missing angles. Show your work! Be ready to discuss your answer.

Answer 1

a = 35 b = 25

Explanation:

Triangles always add up to 180 degrees. Knowing this we can first solve the triangle with the right angle.

55 + 90 + a = 180

Before we solve this, keep in mind that the reflective property will be used on angle a, giving the answer to the third angle in the second triangle.

145 + a = 180

-145 -145

a = 35

Now that we have a solved use the reflective property to get it on the second triangle.

120 + 35 + b = 180

155 + b = 180

-155 -155

b = 25

There you have your two angles.

Hope this helped you out.

Answer 2

For a.

Since there are already two angles given for the triangle, we can measure the last angle using this formula:

90 + 55 + a = 180

Now solve for "a".

90 + 55 + a = 180

145 + a = 180

a = 180 - 145

a = 35°

For b.

From the picture above, the two triangle's tip are touching and having to form vertical angles. This means that the angles are congruent to each other.

Now that we have two angles in the second triangle(35 and 120), we can use the same formula:

35 + 120 + b = 180

Now solve for "b":

35 + 120 + b = 180

155 + b = 180

b = 180 - 155

b = 25°