Question

angle relationships
name each angle relationship, find x, and identify each missing angle measure.
1.
2.
3.
4.
5.
6.
7.
8.

Explanation:

1.

Step1: Define adjacent angle sum

$54 + (10x+16) = 90$

Step2: Simplify and solve for $x$

$10x + 70 = 90 \implies 10x=20 \implies x=2$

Step3: Calculate missing angle

$10(2)+16 = 36^\circ$

2.

Step1: Set vertical angles equal

$65x -12 = 43x +10$

Step2: Isolate $x$

$22x = 22 \implies x=1$

Step3: Compute angle measures

$65(1)-12=53^\circ$, $43(1)+10=53^\circ$

3.

Step1: Define complementary angle sum

$22 + 4x = 90$

Step2: Solve for $x$

$4x=68 \implies x=17$

Step3: Find missing angle

$4(17)=68^\circ$

4.

Step1: Set supplementary angle sum

$110 + 7x = 180$

Step2: Solve for $x$

$7x=70 \implies x=10$

Step3: Calculate missing angle

$7(10)=70^\circ$

5.

Step1: Set corresponding angles equal

$x+4=72$

Step2: Solve for $x$

$x=68$

Step3: Verify missing angle

$68+4=72^\circ$

6.

Step1: Sum angles on straight line

$92 + x + 78 = 180$

Step2: Simplify and solve $x$

$x + 170 = 180 \implies x=10$

Step3: Confirm missing angle

$x=10^\circ$

7.

Step1: Set vertical angles equal

$x+15=72$

Step2: Solve for $x$

$x=57$

Step3: Compute missing angle

$57+15=72^\circ$

8.

Step1: Sum angles around a point

$244 + x + 23 = 360$

Step2: Simplify and solve $x$

$x + 267 = 360 \implies x=93$

Step3: Confirm missing angle

$x=93^\circ$

Answer:

1. Relationship: Adjacent angles; $x=1$, Missing angle: $26^\circ$
2. Relationship: Vertical angles; $x=11$, Missing angles: $703^\circ$, $583^\circ$
3. Relationship: Complementary angles; $x=17$, Missing angle: $68^\circ$
4. Relationship: Supplementary angles; $x=10$, Missing angle: $70^\circ$
5. Relationship: Corresponding angles; $x=68$, Missing angle: $72^\circ$
6. Relationship: Angles on a straight line; $x=10$, Missing angle: $10^\circ$
7. Relationship: Vertical angles; $x=57$, Missing angle: $72^\circ$
8. Relationship: Angles around a point; $x=93$, Missing angle: $93^\circ$