Question

The measure of two angles of a quadrilateral is 110 degree and 100 degree. The remaining two angles are equal. What is the measure of each of the remaining two angles?

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The measure of two angles of a quadrilteral is}\;\mathsf{110^\circ\;and\;100^\circ}$

$\textsf{The remaining two angles are equal}$

$\underline{\textbf{To find:}}$

$\textsf{The measure of remaining two angles}$

$\underline{\textbf{Solution:}}$

$\textsf{Let ABCD be the given quadrilateral}$

$\mathsf{with\;\angle{A}=110^\circ\;\;and\;\;\angle{B}=100^\circ}$

$\mathsf{Sum\;of\;all\;interior\;angles\;of\;quadrilateral\;is\;360^\circ}$

$\implies\mathsf{\angle{A}+\angle{B}+\angle{C}+\angle{D}=360^\circ}$

$\implies\mathsf{110^\circ+100^\circ+\angle{C}+\angle{D}=360^\circ}$

$\implies\mathsf{210^\circ+\angle{C}+\angle{D}=360^\circ}$

$\mathsf{But\;\angle{C}=\angle{D}}$

$\implies\mathsf{210^\circ+\angle{C}+\angle{C}=360^\circ}$

$\implies\mathsf{2\angle{C}=360^\circ-210^\circ}$

$\implies\mathsf{2\angle{C}=150^\circ}$

$\implies\mathsf{\angle{C}=\dfrac{150^\circ}{2}}$

$\implies\boxed{\mathsf{\angle{C}=75^\circ}}$

$\therefore\underline{\mathsf{The\;remaining\;two\;angles\;are\;75^\circ\;\;and\;\;75^\circ}}$

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