Answer:
Question 7: m∠ x° = 108°
Question 8: m∠ x° = 48°
Question 9: m∠ x° = 8°
Step-by-step 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.
