TEKS 6.8A Worksheets — Grade 6 Extend previous knowledge of triangles and their

Miguel is building a triangular flowerbed in his backyard in Dallas, Texas. The angles of his flowerbed triangle are represented as follows: one angle measures 50 degrees, and the other angle measures 70 degrees. What is the measure of the third angle in Miguel's triangular flowerbed?

1. 60 degrees ✓
2. 70 degrees
3. 80 degrees
4. 90 degrees

Why: To find the measure of the third angle in a triangle, you subtract the sum of the known angles from 180 degrees. The known angles are 50 degrees and 70 degrees. First, add these two angles together: 50 + 70 = 120 degrees. Then, subtract this sum from 180 degrees: 180 - 120 = 60 degrees. Thus, the measure of the third angle is 60 degrees.

Trinity is helping her family build a new fence around their backyard in Houston. They have three sections of the fence to measure. The first section is 3 1/2 feet long, the second section is 2 3/4 feet long, and the third section is 4 1/8 feet long. What is the total length of the fence they need to build in feet?

1. 10 3/8 ✓
2. 10 1/2
3. 11
4. 11 1/4

Why: To find the total length of the fence, add the lengths of the three sections. First, convert each mixed number to an improper fraction: 3 1/2 = 7/2, 2 3/4 = 11/4, and 4 1/8 = 33/8. The least common denominator for these fractions is 8. Convert each fraction: 7/2 = 28/8, 11/4 = 22/8, and 33/8 remains the same. Now, add the fractions: 28/8 + 22/8 + 33/8 = 83/8. Convert 83/8 back to a mixed number: 83 ÷ 8 = 10 R3, which gives us 10 3/8. Therefore, the total length of the fence they need to build is 10 3/8 feet.

Luna is building a birdhouse to attract native birds in her backyard in Waco, Texas. She wants to make sure the angles in her birdhouse's triangular roof add up to exactly 180 degrees. If one angle is 70 degrees and the other is 60 degrees, what is the measure of the third angle in degrees?

1. 50 ✓
2. 60
3. 70
4. 80

Why: To find the measure of the third angle, we use the fact that the sum of the angles in a triangle is always 180 degrees. Luna knows two angles: 70 degrees and 60 degrees. First, we add those two angles together: 70 + 60 = 130 degrees. Then, to find the third angle, we subtract this sum from 180 degrees: 180 - 130 = 50 degrees. Therefore, the measure of the third angle is 50 degrees.

Riley is creating a triangular flower bed in her backyard in Texas. The first angle of the triangle measures 45 degrees, and the second angle measures 75 degrees. What is the measure of the third angle in the triangle?

1. 60 ✓
2. 75
3. 90
4. 105

Why: To find the measure of the third angle in a triangle, recall that the sum of the angles in a triangle is always 180 degrees. Here, we add the measures of the first two angles: 45 + 75 = 120 degrees. Then, we subtract this sum from 180 degrees to find the third angle: 180 - 120 = 60 degrees. Therefore, the measure of the third angle is 60 degrees.

Luis is designing a triangular garden in Austin, Texas. One angle of the triangle measures 50 degrees, and another angle measures 70 degrees. What is the measure of the third angle in his garden design?

1. 60 degrees ✓
2. 70 degrees
3. 80 degrees
4. 90 degrees

Why: To find the measure of the third angle in a triangle, you can use the fact that the sum of all angles in a triangle is always 180 degrees. Here, you add the two known angles: 50 degrees + 70 degrees = 120 degrees. Next, subtract this sum from 180 degrees: 180 degrees - 120 degrees = 60 degrees. Therefore, the measure of the third angle is 60 degrees.

Roberto is helping his dad build a triangular flower bed in their backyard in Fredericksburg. The flower bed will have one angle of 50 degrees and another angle of 70 degrees. What is the measure of the third angle in the flower bed?

1. 60 degrees ✓
2. 70 degrees
3. 80 degrees
4. 90 degrees

Why: To find the measure of the third angle in a triangle, you can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees. First, add the two known angles: 50 degrees + 70 degrees = 120 degrees. Then, subtract this sum from 180 degrees to find the third angle: 180 degrees - 120 degrees = 60 degrees. Therefore, the measure of the third angle is 60 degrees.

Omar is working on a project about the wildlife in Texas. He learns that the angles of a triangle represent the habitat areas of three animals: the white-tailed deer, the great horned owl, and the javelina. If the angle representing the white-tailed deer is 75 degrees and the angle for the great horned owl is 45 degrees, what is the measure of the angle representing the javelina?

1. 60 degrees ✓
2. 90 degrees
3. 45 degrees
4. 30 degrees

Why: To find the missing angle in a triangle, we use the Triangle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees. Here, Omar has the angles of 75 degrees and 45 degrees. First, add these two angles together: 75 + 45 = 120 degrees. To find the missing angle, subtract this sum from 180 degrees: 180 - 120 = 60 degrees. Therefore, the angle representing the javelina is 60 degrees.

Eduardo is designing a triangular garden in his backyard in Texas. He knows that one angle measures 35 degrees and another angle measures 75 degrees. What is the measure of the third angle in Eduardo's triangular garden?

1. 70 degrees ✓
2. 80 degrees
3. 90 degrees
4. 100 degrees

Why: To find the measure of the third angle in a triangle, we can use the fact that the sum of all angles in a triangle is 180 degrees. First, add the two known angles: 35 degrees + 75 degrees = 110 degrees. Then, subtract this sum from 180 degrees: 180 degrees - 110 degrees = 70 degrees. Therefore, the measure of the third angle is 70 degrees.