Question

Please help me I’m been trying to do this for 30 mins

Answer 1

a triangle's angle will always sum up to 180°

In question 7, you can easily find X by first adding 36 + 36. This sums up to 72°. Now you have to subtract 72° from 180°. X = 108°

For question 9, X = 132°

Question 8, X = 58°>

Hope this helps

Answer 2

Question 7: m∠ x° = 108°

Question 8: m∠ x° = 48°

Question 9: m∠ x° = 8°

Explanation:

Regardless of the type of triangle you are dealing with, always remember that the sum of the measures of any triangle is 180°.

Question 7

Given the two angles of a triangle: ∠36° and ∠36°, then it means that m∠ x° is:

m∠ x° = 180° - 36° - 36°

m∠ x° = 108°

Therefore, the value of x = 108°. Since two of its angles have the same measure of 36°, then it means that the given triangle is an isoceles triangle. Also, since once of its angles has a measure that is greater than 90°, then the triangle is also an obtuse triangle. In other words, the given triangle is an obtuse isoceles triangle.

Note:

Another way of solving question 7 is to add the two given measures of angle and subtract their sum from 180°.

Question 8

Simiar to question 7, you could simply add the two given measures of a triangle, °42 and 90°, and subtract their sum from 180° to find the value of x.

m∠ x° = 180° - (42° + 90°)

m∠ x° = 180° - 132°

m∠ x° = 48°

Therefore, the value of x = 48°. Since one of its angles has a measure of 90°, then it means that it is a right triangle. Also, since none of its angles have the same measure, then it means that the given triangle is a scalene triangle. In other words, the given triangle is a scalene right triangle.

Question 9

The easiest way of solving this given problem is to solve for x algebraically. We can set up the following equation to solve for x:

180° = m∠ x° + m∠ 126° + m∠ 22°

180° = 4x° + 126° + 22°

180° = 4x° + 148°

Subtract 148° from both sides:

180° - 148° = 4x° + 148° - 148°

32° = 4x°

Divide both sides by 4 to solve for x:

32°/4 = 4x°/4

8 = x

Hence, the value of x = 8°. Verify whether we have the correct value for x by substituting its value to the equation:

180° = 4x° + 126° + 22°

180° = 4(8)° + 126° + 22°

180° = 32° + 126° + 22°

180° = 180° (True statement).

Since none of the three angles have the same measure (scalene), and that one of the angles is greater than 90° (obtuse). Therefore, the given triangle is an obtuse scalene triangle.