Question

11.
these two angles are:
supplementary _____
complementary _____
angle x = _____

12.
these two angles are:
supplementary _____
complementary _____
angle x = _____

given: ∠1 = 90°
∠2 = 34°
∠6 = 137°

1. ∠3 = ______°

1. ∠8 = ______°

1. ∠4 = ______°

Explanation:

Problem 11:

Step1: Identify angle relationship

The angles form a straight line (180°), so they are supplementary.

Step2: Calculate angle x

$x = 180^\circ - 85^\circ$
$x = 95^\circ$

Problem 12:

Step1: Identify angle relationship

The angles add to 90° (right angle), so they are complementary.

Step2: Calculate angle x

$x = 90^\circ - 32^\circ$
$x = 58^\circ$

Problem 13:

Step1: Use straight angle sum

$\angle 1 + \angle 2 + \angle 3 = 180^\circ$

Step2: Solve for $\angle 3$

$\angle 3 = 180^\circ - 90^\circ - 34^\circ$
$\angle 3 = 56^\circ$

Problem 14:

Step1: Use vertical angle property

$\angle 8 = \angle 2$

Step2: Assign value to $\angle 8$

$\angle 8 = 34^\circ$

Problem 15:

Step1: Use supplementary angle property

$\angle 4 + \angle 2 = 180^\circ$

Step2: Solve for $\angle 4$

$\angle 4 = 180^\circ - 34^\circ$
$\angle 4 = 146^\circ$

Answer:

1. These two angles are: Supplementary $\boldsymbol{\checkmark}$, Complementary $\square$, Angle x = $\boldsymbol{95^\circ}$
2. These two angles are: Supplementary $\square$, Complementary $\boldsymbol{\checkmark}$, Angle x = $\boldsymbol{58^\circ}$
3. $\boldsymbol{56}$
4. $\boldsymbol{34}$
5. $\boldsymbol{146}$