Question

in a rhombus ABCD ,angle DAC =45°.Find the measures of the following angles a) angles ACB b) ADB c) ABC ​

Answer 1

Step-by-step explanation:

Given in a rhombus ABCD ,angle DAC =45°.Find the measures of the following angles a) angles ACB b) ADB c) ABC  

• Now ABCD is a rhombus  
• Angle ADC = ABC (opposite angles are equal
• Angle DAC = 45 degree
• Let angle ADB = x
• Now diagonals of rhombus bisect each other at right angles.
• So angle AOD = 90 degree
• Now AB is parallel to CD
• So angle ACB = DAC = 45 degree (alternate interior angles)
• So in triangle AOD we have,
•        So x + 45 + 90 = 180 (angle sum property of triangle)
•          Or x + 135 = 180
•           Or x = 180 – 135
•            Or x = 45 degree
• So ADB = 45 degree, angle ACB = 45 degree and angle ABC = 45 degree

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https://brainly.in/question/13951142