The diagonal AC and BD of a parallelogram ABCD intersect each other at point O. If angle DAC=32° and angle AOB=70°,then what is the measure of angle DBC?Choices:- 24° 86° 38° 32°
Question
The diagonal AC and BD of a parallelogram ABCD intersect each other at point O. If angle DAC=32° and angle AOB=70°,then what is the measure of angle DBC?Choices:- 24° 86° 38° 32°
Solution
In a parallelogram, opposite angles are equal. Therefore, angle DAC = angle BCD = 32°.
In triangle AOB, the sum of the angles is 180°. Therefore, angle BOA = 180° - 70° - 32° = 78°.
Since the diagonals of a parallelogram bisect each other, triangle BOA is congruent to triangle COD. Therefore, angle COD = angle BOA = 78°.
In triangle BCD, the sum of the angles is 180°. Therefore, angle DBC = 180° - 32° - 78° = 70°.
So, the measure of angle DBC is 70°.
Similar Questions
Assertion : ABCD is a square. AC and BD intersect at “O “. The measure of ∠ AOB= 90°.Reason : Diagonals of a square bisect each other at right angles.
Identify the angle of 𝑥° in the parallelogram.A. 26°B. 42°C. 68°D. 118°
Question No 48.In right ΔABC, where ∠C is the right angle, point D lies on side AB, and point E lies on side BC such that AC = CD, DE = EB, and the ratio AC : DE = 4 : 3. What is the ratio AD : DB?
ABCD is a rhombus such that one of its diagonals is equal to its side. Find the measure of the angles of rhombus ABCD.
Consider rectangle ABCD with diagonals BD and AC intersecting at E. Rectangle A B C D has diagonals B D and A C that intersect at the center of the rectangle at point E. Angles B C E is 52 degrees, angle C B E is 52 degrees, angle D E A is 104 degrees, and angle B E A is 76 degrees. Which is true about the angle relationships in the rectangle? Check all that apply. AngleBEA and AngleCED are vertical angles and equal 104°. AngleABE and AngleCBE are complementary angles. AngleBEC and AngleCED are vertical angles. AngleBEA and AngleAED are supplementary angles whose sum is 180°. AngleBEC and AngleAED are adjacent angles.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.