Question

In the diagram, what is the measure of angle 1 to the nearest degree?

82°
92°
94°
98°

Answer 1

7x+4=88
7x=84
x=12
7x-12=7*(12)-2=82
angle 1=180-82=98

Answer 2

`m<1=98\°`

Explanation:

Step 1

Find the value of x

we know that

`(7x+4)\°=88\°` ----> by vertical angles

Solve for x

`7x=88-4`

`x=84/7=12\°`

Step 2

Find the measure of angle 1

we know that

`m<1+(7x-2)\°=180\°` ------> by supplementary angles

Substitute the value of x and solve for m<1

`m<1+(7(12)-2)\°=180\°`

`m<1=180\°-82\°`

`m<1=98\°`