If m∠2=40°, what is the measure of ∠1 + ∠6?

180°

Step-by-step explanation:

The diagram for this question has been attached to this response.

From the diagram;

(i) ∠2 and ∠6 are equal since they are corresponding angles. This implies that the measure of angle 2 (m∠2) is equal to the measure of angle 6 (m∠6). i.e

m∠2 = m∠6       ---------(a)

But m∠2 = 40°

Substitute this into equation (a) as follows;

40° = m∠6

∴ m∠6 = 40°

(ii) ∠1 and ∠2 are supplementary. This implies that the sum of the measures of angle 1 (m∠1) and angle 2(m∠2) is equal to 180°. i.e

m∠1 + m∠2 = 180°      ------------------(b)

But m∠2 = 40°

Substitute this into equation (b) as follows;

m∠1 + 40° = 180°

m∠1 = 180° - 40°

m∠1 = 140°

(iii) The measure of ∠1 + ∠6 is given by;

m∠1 + m∠6

Substitute the values of m∠1 = 140° and m∠6 = 40° into the expression to get

m∠1 + m∠6 = 140° + 40°

m∠1 + m∠6 = 180°

Therefore the measure of  ∠1 + ∠6 is 180°

equal to

step-by-step explanation:

step-by-step :