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Given: m∠A + m∠B = m∠B + m∠C

Prove: m∠A = m∠C


Starting with our given statement, m∠A + m∠B = m∠B + m∠C, we can use the subtraction property of equality to subtract m∠B from each side:


m∠A + m∠B - m∠B = m∠B + m∠C - m∠B


When we subtract something from itself, it equals 0. This leaves us with:


m∠A + 0 = m∠C + 0


Adding 0 to anything leaves it as it was. This gives us:

m∠A= m∠C

From the given data it has been proved that \(\rm \angle A = \angle C\) by using the arithmetic operation that is , subtraction property.

Given :

\(\rm \angle A + \angle B = \angle B + \angle C\)

The following steps that prove \(\rm \angle A = \angle C\) are given below:

Step 1 - Rewrite the given expression.

\(\rm \angle A + \angle B = \angle C + \angle B\)

Step 2 - Observe the given expression and find the angle on both sides that are same.

Step 3 - Subtract the same angle on both the sides, that is, subtract \(\rm \angle B\).

\(\rm \angle A + \angle B - \angle B = \angle C + \angle B - \angle B\)

Step 4 - Further simplify the above expression.

\(\rm \angle A = \angle C\)

From the above steps it is proved that \(\rm \angle A = \angle C\).

For more information, refer the link given below:

https://brainly.com/question/25018625

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