If m angle DEF = (6x+37) and mFGD = (19x-31), find m angle DEF

Step-by-step explanation:

Given:

We need to find the m ∠ DEF.

Solution:

Now we can say that;

By inscribed angle theorem;

"The measure of the angle is twice the measure on the arc subtended by it."

so we get;

Applying distributive property we get;

Combining the like terms we get;

Dividing both side by 7 we get;

Hence

The correct option is;

The sum of angles A and B are supplementary to angle C

Step-by-step explanation:

The statements are analysed as follows

1. Angle A is congruent to itself reflective property

Which shows that ΔABC and ΔADE have a common and equal angle

2. Segment ED and CB are parallel

From the transversal line passing EB and CB which shows that the angles ∠ADE and ∠ABC are equal and also ∠AED and ∠ACB are equal

The statement is used to prove similarity between the ΔABC and ΔADE

3. The sum of angles A and B are supplementary to angle C

The above statements relates to only ΔABC and i does not show similarity between ΔABC and ΔADE.