ABCD is a rectangle. On line segment AB, E is a point such that ∠ADE=17∘ and ∠BCE=29∘. What is the measure of ∠DEC (in degrees)?
∠ADE = 90-17 = 73°
∠ECD = ∠CEB = 29°
∠DEC = 180 - (73+29) = 78°
# 5 from HW
Given: x is the midpoint AY, and Y is the midpoint of XB.
Prove: AX YB
Satements
A
XY
Reasons
B
1.
2.
3.
To find the measure of angle DEC, we need to use the properties of a rectangle.
Since ABCD is a rectangle, opposite angles are congruent. So, angle BCD is congruent to angle DAB.
Let's use this information to find the measure of angle DEC.
1. Since angle DAB is congruent to angle BCD, we know that angle DAB + angle BCD = 180°.
2. We are given that angle DAB = 17°. So, we can rewrite the equation as 17° + angle BCD = 180°.
3. Now, let's find angle BCD. We are given that angle BCE = 29°, and since ABCD is a rectangle, opposite angles are congruent. So, angle BCD = angle BCE = 29°.
4. Substituting the value of angle BCD in the equation, we have 17° + 29° = 180°.
5. Simplifying the equation, we have 46° = 180°.
6. Finally, to find angle DEC, we need to subtract angle DAB (17°) from the sum of 180° and angle BCD (29°).
Angle DEC = 180° - (17° + 29°)
= 180° - 46°
= 134°.
Therefore, the measure of angle DEC is 134°.