Question

Two angles form a linear pair. The measure of the smaller angle is one half the measure of the larger angle. What is the degree measure of the large angle?

Answer 1

The larger angle measures at `120^o`.
The smaller one is `60^o` (one half of a larger angle).
Their sum is `180^o`, as it should for a linear pair.

Explanation:

Assume a larger angle measure `X^o` and a smaller one measure `Y^o`.
Linear pair of angle consists of two angles, sum of which is `180^o`.
Therefore,
`X+Y=180`.
Since a smaller angle measure as half of a larger one,
`Y=1/2X`

We have a system of two linear equations with two unknowns.
Substitute `Y` from the second equation intot the first one anf find `X`:
`X+1/2X=180`
`3X=360`
`X=120` - this is a larger angle.

Now we can find `Y`:
`Y=1/2*120=60` - this is a smaller angle.