Question

Find the measures of the numbered angles in the kite.

Answer 1

m1=m2 = 111 degrees

Explanation:

1. construct a line between angles 1 and 2

//now we have 2 triangles. They are both isoscles triangles.

3. m(base angles in 90 triangle) = (180-90)/2 = 45 degrees. (base angle th.)

4. m(base angles in 48 triangle) = (180-48)/2 = 66degrees. (base angle th.)

5. m1 = 66+ 45 = 111 degrees. (algebra)

6. m2=m1 = 66+45 =111 degrees (algebra)

check:

sum of all angles has to add up to 360 degrees.

48 + 90+ 111+111=360

360=360

Answer 2

The measure of the numbered angles in the kite is:

• m∠1 = 111°

• m∠2 = 111°

The sum of the angles in any quadrilateral is 360 degrees. Let's use this information to find the measures of angles 1 and 2 in the kite.

Identify angles:

We know angles 1 and 2 are opposite angles in the kite, so they are congruent.

We also see two right angles (90 degrees) in the figure.

Set up equation:

Since the sum of angles in a quadrilateral is 360 degrees, we can write an equation:

48°+ 90°+ m∠1 + m∠2 = 360

Given that m∠1 = m∠2

Combine like terms:

2m∠1 + 138° = 360°

4. Solve for m∠1:

Subtract 138° from both sides:

2m∠1 = 222°

Divide both sides by 2:

m∠1 = 111°

5. Conclusion:

Therefore, both m∠1 and m∠2 are:

m∠1 = 111°

m∠2 = 111°