If m∠3 = 54°, find the measure of each missing angle.

Uisbg multiple line and angle theorems, the values of each of the 14 angles are given.

Using the geometry theorems :

1.)

∠2 is a right angle = 90°

2.)

∠1 + ∠2 + ∠3 = 180° (sum of angle on a straight line)

90 + ∠1 + 54° = 180°

∠1 = (180 - 144) = 36°

(∠2 and ∠5) ; (∠3 and ∠6) ; (∠1 and ∠4) are vertically opposite ;

Hence,

∠4 = 36°

∠5 = 90°

∠6 = 54°

∠3 = ∠8 = 54° (corresponding angles)

∠9 + ∠8 = 180° (sum of angle on a straight line)

∠9 = (180 - 54) =126°

∠7 = ∠9 = 126° (vertically opposite angles)

∠8 = ∠10 = 54° (vertically opposite angles)

∠4 = ∠13 = 36° (corresponding angles )

∠12 + ∠13 = 180° (sum of angle on a straight line)

∠12 = (180 - 36) =126°

∠11 = ∠13 = 36° (vertically opposite angles)

∠12 = ∠14 = 126° (vertically opposite angles)

Learn more about angles :brainly.com/question/18868430?referrer=searchResults

Final answer:

To find the measure of the missing angles, use the fact that the sum of angles in a triangle is 180 degrees. Substitute the given value and solve for the missing angles. The measure of each missing angle is 126 degrees.

Explanation:

To find the measure of the missing angle, we can use the fact that the sum of angles in a triangle is 180 degrees. Since we know that m∠3 = 54°, and angles 1 and 2 are adjacent angles, we can use the equation:

m∠1 + m∠2 + m∠3 = 180

Substituting the given value for m∠3, we get:

m∠1 + m∠2 + 54 = 180

Now we can solve for the missing angles by rearranging the equation:

m∠1 + m∠2 = 180 - 54

m∠1 + m∠2 = 126

So, the measure of each missing angle is 126 degrees.

Learn more about Triangles here:

brainly.com/question/29083884

#SPJ3