Triangles with and Extended Angle - How it Works - Video

Example 1

Example 1:

In this example we need to find x. It is inside the triangle. The triangles is comprised of 3 angles (orange, green, and yellow). The first one we find is the yellow angle (<BCA). We use the fact that yellow (<BCA) + blue (<BCQ) form a linear pair, 180°. So we have ==> yellow angle + 122° = 180°. Next we subtract the term 122° from each side ==> yellow (<ACB) = 58°.

Now we need to find x or the green angle (<ABC). We use the fact that the sum of the angles in a triangle is 180°.

Next we use ==> orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) = 180°.

Now, we substitute what we know in the equation ==> 68° + x + 58° = 180° then x + 126° = 180° after adding 68° and 58°.

Then x = 54° after we subtract 126° on both sides.

So our final answer is x = 54°.

Example 2

Example 2:

In this example we need to find x. It is inside the triangle. The triangle is comprised of 3 angles (orange, green, and yellow). The first one we find is the yellow angle (<BCA). We can do that because triangle ABC is an isosceles triangle, so the orange and yellow angles are congruent, because those are the base angles. Next we can the find the blue angle (<BCQ) or the green angle (<ABC), we get to choose.

Now, we use the facts that yellow (<BCA) + blue (<BCQ) form a linear pair, 180°. So we have ==> the yellow angle + 61° = 180°.

Next we subtract the term 61° from each side ==> yellow (<BCA) = 119°.

Now we have the first answer, y = 119°.

Next we need to find x or the green angle (<ABC). We use the fact that the sum of the angles in a triangle is 180°.

So we use the fact that ==> the orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) = 180°.

Now, we substitute what we know into that to get 61° + x + 61° = 180° then x + 122° = 180° then x = 58° after we subtract 122° on both sides.

So our final answer is x = 58° and y = 119°.

Example 3

Example 3:

In this example we need to find x. It is inside the triangle. The triangle is comprised of 3 angles (orange, green, and yellow). Since triangle ABC is an equilateral triangle, each angle is 60°, because 60° + 60° + 60° = 180°.

Now, we use the facts that yellow (<BCA) + blue (<BCQ) form a linear pair, 180°. So we have ==> 60° + blue angle = 180°.

Next we subtract the term 60° from each side ==> yellow (<BCA) = 120°. Now we have the first answer, y = 120°.

Now, we use the facts that purple (<MAB) + orange (<BAC) form a linear pair, 180°. So we have ==> purple angle + 60° = 180°.

Next we subtract the term 60° from each side ==> yellow (<MAB) = 120°. Now we have the second answer, x = 120°.

So our final answer is x = 120° and y = 120°.

Example 4

Example 4:

In this example we need to find x. It is inside the triangle. The triangle is comprised of 3 angles (orange, green, and yellow). The first ones, we find are the orange angle (<BAC) and the yellow angle (<BCA). We can find both angles at the same time since triangle ABC is an isosceles triangle and the orange and yellow angles are the base angles. And remember base angles are the same in an isosceles triangle.

We use the fact that the sum of the angles in a triangle is 180°.

Now we can use the fact ==> orange angle (<CAB) + green angle (<ABC) + yellow angle (<BCA) = 180°.

Now, we substitute what we know into that to get <CAB + 40° + <BCA = 180°.

Next, we subtract 40° on both sides ==> <CAB + <BCA = 140°.

We can either divide 140° by 2 to find the value of each angle or can mentally find what number that adds together to get 140°. After doing that, we know each angle is 70°.

Now, we use the facts that yellow (<BCA) + blue (<BCQ) form a linear pair, 180°.

So we have ==> 70° + blue angle = 180°. Next we subtract the term 70° from each side ==> yellow (<BCA) = 110°.

Now we have the first answer, y = 110°. So our final answer is x = 110°.

Live Worksheet

Here is the link if you prefer.