Math  /  Geometry

Question(7)
Angles in parallel lines Q1 - Alternate, co-interior or corresponding Laura Jemiolo
Q1 06\frac{0}{6} Q2 08\frac{0}{8} x=x= \square - [1]
Total x=x= \square 014\frac{0}{14} x=x= \square [1] x=x= \square [1] x=0x=\square 0 [1] x=x= \square [1] Mark it

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx in six different diagrams, where parallel lines are crossed by another line, using angle rules. Watch out! Don't mix up the angle rules!
Corresponding angles are equal, alternate angles are equal, but co-interior angles add up to 180180^\circ.

STEP 2

1. Angle Relationships
2. Calculate xx

STEP 3

The given angle is 126126^\circ, and it's *co-interior* with xx.
Co-interior angles add up to 180180^\circ.

STEP 4

The given angle is 113113^\circ, and it's *corresponding* with xx.
Corresponding angles are equal.

STEP 5

The given angle is 120120^\circ, and it's *alternate* with xx.
Alternate angles are equal!

STEP 6

We've got 7979^\circ, and it's *co-interior* with xx.
Remember, co-interior angles add to 180180^\circ.

STEP 7

The given angle is 137137^\circ, and it's *corresponding* with xx.
Corresponding angles are the same.

STEP 8

Here, we have 7070^\circ, and it's *alternate* with xx.
Alternate angles are equal.

STEP 9

126+x=180126^\circ + x = 180^\circ Subtract 126126^\circ from both sides: x=180126x = 180^\circ - 126^\circ x=54x = \textbf{54}^\circ

STEP 10

Since the angles are corresponding: x=113x = \textbf{113}^\circ

STEP 11

Alternate angles are equal, so: x=120x = \textbf{120}^\circ

STEP 12

Co-interior angles add to 180180^\circ: 79+x=18079^\circ + x = 180^\circ Subtract 7979^\circ from both sides: x=18079x = 180^\circ - 79^\circ x=101x = \textbf{101}^\circ

STEP 13

Corresponding angles are equal, so: x=137x = \textbf{137}^\circ

STEP 14

Alternate angles are equal, so: x=70x = \textbf{70}^\circ

STEP 15

Diagram 1: x=54x = 54^\circ Diagram 2: x=113x = 113^\circ Diagram 3: x=120x = 120^\circ Diagram 4: x=101x = 101^\circ Diagram 5: x=137x = 137^\circ Diagram 6: x=70x = 70^\circ

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