If the consecutive angles of a parallelogram are in the ratio \(2:3\), what is the measure of the smaller angle?
72°
Consecutive angles of a parallelogram are supplementary, i.e., they add up to \(180°\).
Let the angles be \(2x\) and \(3x\), so \(2x + 3x = 180° \Rightarrow 5x = 180° \Rightarrow x = 36°\).
The smaller angle \(= 2x = 2 \times 36° = 72°\).
Hence, the smaller angle measures 72°.
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Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
