Question

the measures of two adjacent angle of quadrilateral are 125° and 35° and the other two angles are equal . find the measure of each of the equal angles​

Answer 1

Step-by-step explanation:

total measure of quadrilateral is 360°

so, two angles are 125 and 35

other two angles are equal

so we take that two Angles as X and X

so,

125+35+X+X = 360°

160+2x = 360°

2x = 360-160

2x = 200°

X = 100°

another two angles are 100° and 100°

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Answer 2

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

• The measures of two adjacent angle of quadrilateral are 125° and 35° and the other two angles are equal . find the measure of each of the equal angles

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

• First Adjacent Angle = $\sf\green{ 125°}$
• Second Adjacent Angle = $\sf\green{ 35°}$
• Angle C = Angle D

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

Angle Sum Property Of Quadrilateral

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \angle \: A \: + \angle \: B \: + \angle \: C \: + \angle \: D \: = \: 360 }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{125 \: + \: 35 \: + \: \angle \: C \: + \: \angle \: D \: = \: 360 }}$

Angle C = Angle D ( Given )

$\qquad \quad {:} \longrightarrow \sf{\sf{160\: + \: 2\angle \: C \: = \: 360 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 2\angle C \: = \: 360 \: - \: 160}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 2\angle C \: = \: 200}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: \angle C \: = \: \cancel\frac{200}{2} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \:\angle C \: = \: 100° }}}$

Angle C = Angle D = 100°

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \angle \: A \: + \angle \: B \: + \angle \: C \: + \angle \: D \: = \: 360 }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{125 \: + \: 35 \: + \: 100 \: + \: 100 \: = \: 360 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{160 \: + \: 200 \: = \: 360 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \: 360° \: = \: 360° }}}$

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$\large\underline { \underline{ \sf \maltese \red{ \: Measures \: of \: Angles \: :- }}}$

$\bf \therefore \; \angle \: A = 125°$

$\bf \therefore \; \angle \: B = 35°$

$\bf \therefore \; \angle \: C = 100°$

$\bf \therefore \; \angle \: D= 100°$

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Diagram:-

• Diagram is in attachment.

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