Question

d) one angle of parallelogram
parallelogram is 100° Find
the measures of the remaining
three angles.​

Answer 1

Answer:

since it's a parallelogram with one side 100°

the side opposite is 80°,opposite angles are supplementary....

using this step u can find all the other sides as 100°,80°,100°, and 80°

hope it helps

Answer 2

$\underline{\textsf{\textbf{\purple{ \mapsto Given:}}}}$

• There is a parallelogram.
• One angle of a parallelogram is 100° .

$\underline{\textsf{\textbf{\purple{ \mapsto To\:Find:}}}}$

• Measure of remaining angles .

$\underline{\textsf{\textbf{\purple{ \mapsto Concept\:Used:}}}}$

• We know that sum of adjacent angles of a parallelogram is 180° .
• Opposite angles of a parallelogram are equal.

$\underline{\textsf{\textbf{\purple{ \mapsto Answer:}}}}$

$\setlength{\unitlength}{15}\begin{picture}(0, 0) \put(1, 1){\line(1, 2){2}}\put(1, 1){\line(1, 0){6}}\put(7, 1){\line(1, 2){2}}\put(2.9,5){\line(1, 0){6}}\put(2.5, 5){ \tt A }\put(9, 5){ \tt B }\put(1, 0.5){ \tt D }\put(7, 0.5){ \tt C }\end{picture}}$

If we imagine a parallelogram ABCD in which ∠BCD = 100° , then

$\tt:\implies \angle ADC + \angle BCD = 180^{\circ}$

$\tt:\implies 100^{\circ}+\angle ADC = 180^{\circ}$

$\tt:\implies \angle ADC = 180^{\circ}-100^{\circ}$

$\underline{\boxed{\red{\tt\longmapsto \angle ADC= 80^{\circ}}}}$

Now ∠ABC and ∠ADC are opposite angles . So they are equal = 80° .

Similarly , ∠DCB = ∠DAB = 100° .

Hence ,

$\boxed{\sf \blue{\bigstar}\:\pink{\angle ABC=\angle ADC = 80^{\circ}}}$

$\boxed{\sf \blue{\bigstar}\:\pink{\angle DCB=\angle DAB = 100^{\circ}}}$