Question

for #13 - 17, find the value of x. 2 pts each
13.
14.
15.
16.
17.

Explanation:

Step1: Use triangle angle - sum property for question 13

The sum of angles in a triangle is \(180^{\circ}\). So, \(x + 37+84 = 180\).

$$x=180-(37 + 84)$$

$$x=180 - 121$$

$$x = 59$$

Step2: Use exterior angle and angle - sum property for question 14

The exterior angle is \(66^{\circ}\). Let the two non - adjacent interior angles be \(y\) (equal to the other base angle as it's an isosceles triangle formed by the exterior angle property) and \(x\). The exterior angle \(66^{\circ}\) is equal to the sum of the two non - adjacent interior angles. Since the triangle is isosceles (the two base angles are equal), \(x=180-2\times(180 - 66)\)
First, find the base angle: \(180 - 66=114\) (supplementary angle to the exterior angle). Then the base angle of the inner triangle \(y = 180-114=66\). Using angle - sum property of triangle \(x+2y=180\), \(x = 180-2\times66=48\)

Step3: Use right - triangle angle - sum property for question 15

In a right - triangle (\(90^{\circ}\) angle), the sum of the two non - right angles is \(90^{\circ}\). So \(x+49 = 90\)

$$x=90 - 49$$

$$x = 41$$

Step4: Use exterior angle property for question 16

The exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles. So \(x=92 + 55\)

$$x=147$$

Step5: Use exterior angle and angle - sum property for question 17

The exterior angle \(86^{\circ}\) is equal to the sum of the two non - adjacent interior angles. Let the unknown angle be \(x\). Using angle - sum property of triangle, first find the adjacent interior angle to \(86^{\circ}\) which is \(180 - 86=94^{\circ}\). Then \(x+23+94=180\)

$$x=180-(23 + 94)$$

$$x=180 - 117$$

$$x = 63$$

Answer:

1. \(x = 59\)
2. \(x = 48\)
3. \(x = 41\)
4. \(x = 147\)
5. \(x = 63\)