Question

In a parallelogram ABCD if angle A is equals -2 X + 35 and angle c is equals- 3x - 5 find the value of x and find the measure of angle A b c d

Answer 1

Given:-

• ABCD is a parallelogram.
• ∠DAB = (-2x+35)° & ∠DCB = (-3x-5)°

To Find:-

• Value of All The Angles in parallelogram ABCD.

Solution:-

☞ In A Parallelogram Opposite Angles are Equal.

$→\;{\sf{(-2x+35)° = (-3x-5)°}}$

$→\;{\sf{-2x+3x = -35°-5°}}$

$→\;{\sf{x = -40°}}$

• ∠DAB = (-2×-40°+35°)
• ∠DAB = 80°+35°
• ∠DAB = 115°

${\sf{➝\;∠DAB\;=\;∠DCB\;→\;\Large\red{115°}}}$

☞ In A Parallelogram Adjacent Angles are Supplementary.

$→\;{\sf{∠DAB+∠ABC = 180°}}$

$→\;{\sf{∠ABC+115° = 180°}}$

$→\;{\sf{∠ABC = 180°-115°}}$

$→\;{\sf{∠ABC = 65°}}$

$\sf{➝\;∠ABC\;=\;∠ADC\;→\;\Large\pink{65°}}$

• Angle A = 115°
• Angle B = 65°
• Angle C = 115°
• Angle D = 65°

$\Large{✓}$

Hope It Helps You ✌️