Question

What are the numerical measures of each angle in the diagram? (Picture included)

∠1 and ∠3 ____ degrees

∠2 and ∠4 ____ degrees

Answer 1

a) 29

b) 151

Explanation:

for 1 and 3, we use the property that two opposite angles are equal when they are formed by two intersecting lines.

so,
`\angle1=\angle3`.

this is
`3x-1=2x+9`. now solve for x:

`3x-1=2x+9\\3x-2x=9+1\\x=10`

use that to find either angle.
`\angle1=30-1=29`. so, we have them equal as 29.

for 2 and 4, we use another property that a straight line has 180 degrees. here,
`\angle1+\angle4=180`.

so, we solve for
`\angle4`.

`\angle4=180-29=151`. we also use the first property to find
`\angle4=\angle2.`

thus, we have found the degrees as 151.

Answer 2

<1&<3 = 29⁰

<2&<4=151⁰

Explanation:

1 and 3 are equal since they're vertical opposite angles

2x +9=3x-1

x=10

then,

2(10)+9=29⁰***(<3)

3(10)-1=29⁰*****(<1)

1+4 makes a straight line which is 180⁰

29⁰+4=180⁰

<4=151⁰*****

similarly to 2+3

2+29⁰=180⁰

<2=151⁰*****