Question

A ray of light is reflected when it hits a mirror. The angle at which the light strikes the mirror is the angle of incidence, i. The angle at which the light is reflected is the angle of reflection, r. The angle of incidence and the angle of reflection are congruent. In the diagram below, if m∠ROQ=124, what is the angle of reflection and m∠ROK?

Justify

Answer 1

Angle of reflection =62 degrees

`\angle ROK=90-62=28 degrees`

Explanation:

We are given that a ray of light is reflected when it hits a mirror

We are given that angle ROQ=124 degrees

We have to find the angle of reflection

Angle of incidence is equal to angle of reflection

`\angle i=\angle r`

`\angle i+\ angle r=124 degrees`

Substitute the value angle r= angle i

Then we get

`\angle r+\angle r=124`

By adding then we get

`2 \angle r=124`

`\angle r=(124)/(2)`

By using division property of equality

`\angle r=\angle POR=62 degrees`

Hence, angle of reflection =62 degrees

`\angle POK=90` degrees

`\angle POR+\angle ROK=90`

`\angle ROK+62=90`

`\angle ROK=90-62=28 degrees`