Question

Given the following diagram, find the required measure.

Given: l | | m

m 1 = 140°
m 3 = 50°

m 6 =

304050 90

Answer 1

`m \angle 6 = 90^\circ`

Explanation:

We are given the following in the question:

`l \parallel m\\\angle 1 = 140^\circ\\\angle 3 = 50^\circ`

We have to find the measure of
`\angle 6`.

Angle 1 and angle 2 forms a pair of straight angle. That is the sum of measure of both angle is equal to 180 degrees. Thus, we can write:

`\angle 1 + \angle 2 = 180^\circ\\\text{Putting the measure of angle 1}\\140 + \angle 2 = 180\\\angle 2 = 180-140\\\angle 2 = 40^\circ`

Now,
`\angle 1, \angle 2, \angle 6` forms the three angles of the triangle.

Now, by angle sum property of triangle the sum of all the three angle of the triangle is 180 degrees.

Thus, we can write:

`\angle 2 + \angle 3 + \angle 6 = 180^\circ\\\text{Putting the values}\\40 + 50 + \angle 6 = 180\\\angle 6 = 180 - 40-50\\\angle 6 = 90^\circ`

Measure of angle 6 is 90 degrees.

Answer 2

m∠6 = 90°

Explanation:

∠1 and ∠2 are a linear pair. This means they are supplementary, or their measures sum to 180°. To find m∠2, we subtract m∠1 from 180:

180-140 = 40°

The measure of ∠2 is 40°.

The sum of the measures of the angles in a triangle is 180°. We have ∠2 and ∠3; to find the measure of ∠6, we subtract these two from 180:

180-(40+50) = 180-90 = 90°

m∠6 = 90°