Two angles of a quadrilateral each measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
Solution:
Given two angles of a quadrilateral each measures 75°.
The other two angles are equal.
We have to find the measure of these angles and the type of the quadrilateral.
Consider a quadrilateral ABCD,
Let ∠A = ∠C = 75°
Let the other two angles ∠B = ∠D = x°
We know that the sum of all angles of a quadrilateral is 360 degrees.
So, ∠A + ∠B + ∠C + ∠D = 360°
75° + x + 75° + x = 360°
150° + 2x = 360°
2x = 360° - 150°
2x = 210°
x = 210°/2
x = 105°
The other angles are 105° each.
We know that the opposite angles of a parallelogram are equal.
Therefore, the given quadrilateral is a parallelogram.
✦ Try This: Two angles of a quadrilateral each measure 60° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 164
Two angles of a quadrilateral each measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
Summary:
Two angles of a quadrilateral each measure 75° and the other two angles are equal. The measure of these two angles are 105° each. The possible figure formed is a parallelogram.
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