Question

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

Explanation:

Step1: Use the triangle angle sum property (for 13)

The sum of angles in a triangle is \(180^{\circ}\). So, \(x + 34+51 = 180\).

$$x=180-(34 + 51)=180 - 85=95$$

Step2: Use the triangle angle sum property (for 14)

Let the two equal - base angles be \(y\). Since the sum of angles in a triangle is \(180^{\circ}\), \(x + 2y=180\). Also, if the base angles are \(62^{\circ}\) (assuming isosceles triangle from the figure), \(x=180-2\times62 = 180 - 124=56\)

Step3: Use the right - triangle angle sum property (for 15)

In a right - triangle (\(90^{\circ}\) angle), the sum of angles is \(180^{\circ}\). So, \(x+40 + 90=180\).

$$x=180-(40 + 90)=180 - 130 = 50$$

Step4: Use the exterior - angle property (for 16)

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(x=52+55=107\)

Step5: Use the exterior - angle property (for 17)

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the exterior angle be \(180 - 68=112^{\circ}\). Then \(x+42=112\).

$$x=112 - 42=70$$

Answer:

1. \(95\)
2. \(56\)
3. \(50\)
4. \(107\)
5. \(70\)