Question

practice problems
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find the measure of each angle indicated.
1)
2)
3)
4)
solve for x. sum of the 3 angles is always 180°
5)
6)
combine like terms
solve for x.
7)
8)

Explanation:

Step1: Use triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\).

For problem 1:

Let the unknown angle be \(x\).

$$x + 55^{\circ}+70^{\circ}=180^{\circ}$$

$$x=180^{\circ}-(55^{\circ} + 70^{\circ})$$

$$x = 180^{\circ}-125^{\circ}$$

$$x = 55^{\circ}$$

For problem 2:

Let the unknown angle be \(y\).

$$y+35^{\circ}+85^{\circ}=180^{\circ}$$

$$y=180^{\circ}-(35^{\circ}+85^{\circ})$$

$$y = 180^{\circ}-120^{\circ}$$

$$y = 60^{\circ}$$

For problem 3:

Let the unknown angle be \(z\).

$$z + 80^{\circ}+39^{\circ}=180^{\circ}$$

$$z=180^{\circ}-(80^{\circ}+39^{\circ})$$

$$z = 180^{\circ}-119^{\circ}$$

$$z = 61^{\circ}$$

For problem 4:

Let the unknown angle be \(w\).

$$w+85^{\circ}+35^{\circ}=180^{\circ}$$

$$w=180^{\circ}-(85^{\circ}+35^{\circ})$$

$$w = 180^{\circ}-120^{\circ}$$

$$w = 60^{\circ}$$

For problem 5:

There is a mistake in the original calculation. The triangle has angles \(30^{\circ}\), \(90^{\circ}\), and \((66 + x)^{\circ}\).

$$30^{\circ}+90^{\circ}+(66 + x)^{\circ}=180^{\circ}$$

$$180^{\circ}+x=180^{\circ}$$

$$x = 0^{\circ}$$

For problem 6:

The triangle has angles \(60^{\circ}\), \(90^{\circ}\), and \(30x^{\circ}\).

$$60^{\circ}+90^{\circ}+30x^{\circ}=180^{\circ}$$

$$30x=180 - 150$$

$$30x = 30$$

$$x = 1$$

For problem 7:

The triangle has angles \((x + 44)^{\circ}\), \(55^{\circ}\), and \(90^{\circ}\).

$$x + 44+55+90=180$$

$$x+189 = 180$$

$$x=-9$$

For problem 8:

The triangle has angles \((- 10 + 5x)^{\circ}\), \(40^{\circ}\), and \(90^{\circ}\).

$$-10 + 5x+40+90=180$$

$$5x+120 = 180$$

$$5x=60$$

$$x = 12$$

Answer:

1. \(55^{\circ}\)
2. \(60^{\circ}\)
3. \(61^{\circ}\)
4. \(60^{\circ}\)
5. \(x = 0^{\circ}\)
6. \(x = 1\)
7. \(x=-9\)
8. \(x = 12\)