Question

In a Parallelogram ABCD , angle D = 115° , determine the measure of Angle A and Angle B​

Answer 1

Answer:

Since the sum of any two consecutive angles of a parallelogram is 180°

Therefore,

∠A+∠D=180°

and ∠A+∠B=180°

Now, ∠A+∠D=180°

∠A+115° =180°

∠A=65°

and, ∠A+∠B=180°

65°+∠B=180

∠B=115°

Thus, ∠A=65°and ∠B=115°.

Explanation:

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Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• In a Parallelogram ABCD , angle D = 115° , determine the measure of Angle A and Angle B

$\large\underline{ \underline{ \sf \maltese{ \: Diagram :- }}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

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$\large\underline{ \underline{ \sf \maltese\red{ \:Basic \: Concept :- }}}$

• The Sum of any Two Consecutive Angles of a Parallelogram is 180°

$\bf\angle \: A \: + \: \angle \: D \: = \: 180°$

$\bf\angle \: A \: + \: \angle \: B \: = \: 180°$

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$\large\underline{ \underline{ \sf \maltese\green{ \: Solution:- }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \angle \: A \: + \: \angle \: D \: = \: 180° }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\bf\: \angle \: D \: = \: 180°( \: given \: )$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: A \: + \: \angle \: D \: = \: 180}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: A \: + \: 115 \: = \: 180 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: A \: = \: 180\: - \: 115 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: A \: = \: 65° }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{\angle\: A \: = \: 65° }}}$

━━━━━━━━━━━━━━━━━━━━━━━━━

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \angle \: A \: + \: \angle \: B\: = \: 180° }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: A \: + \: \angle \: B\: = \: 180}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 65\: + \: \angle \: B\: = \: 180 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: B \: = \: 180\: - \: 65 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: B \: = \: 115° }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{\angle\: B \: = \: 65° }}}$

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$\large\underline{ \underline{ \sf \maltese\green{ \: Verification:- }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \angle \: A \: + \: \angle \: B\: = \: 180}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 65 \: + \: 115 \: = \: 180}}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{180° \: = \: 180° }}}$

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$\quad \qquad\bf \therefore \; \angle \;A = 65°$

$\quad \qquad\bf \therefore \; \angle \;B = 115°$

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