Question

Find the measure of angle a in the figures.
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Answer 1

Answer :-

• Figure A - ∠PRS = a = 140°
• Figure B - ∠WXY = a = 35°
• Figure C - ∠BDE = a = 170°

Given :-

• Figure A - ∠QPR = 80° , ∠PQR = 60°
• Figure B - ∠ZWY = 70° , ∠WYX = 35°
• Figure C - ∠DBC = 25° , ∠BCD = 145°

To Find :-

• Figure A - ∠PRS = a
• Figure B - ∠WXY = a
• Figure C - ∠BDE = a

Explanation :-

In order to solve all these question we need to understand 2 Theorems,

• Exterior Angle Theorem - The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

• Angle Sum Theorem - According to this theorem the sum of all interior angles in a triangle is 180°.

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1. Figure A

➨ In ∆PQR,

↦ ∠QPR + ∠PQR = ∠PRS  

[Exterior Angle Theorem]

↦ 80° + 60° = a

↦ 140° = a

↦ ∠PRS = a = 140°

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2. Figure B

➨ On Line ZX,

↦ ∠ZWY + ∠XWY = 180°     [Liner Pair]

↦ 70° + ∠XWY = 180°

↦ ∠XWY = 180° − 70°

↦ ∠XWY = 110°

➨ In ∆XYZ,

↦ ∠XWY + ∠WYX + ∠WXY = 180°     [Angle sum Theorem]

↦ 110° + 35° + a = 180°    

↦ 145° + a = 180°  

↦  a = 180° − 145°

↦  a = 35°

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3. Figure C

➨ In ∆BCD,

↦ ∠DBC + ∠BCD = ∠BDE

↦ 25° + 145° = a

↦ 170° = a

↦ ∠BDE = a =  170°

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Answer 2

Step-by-step explanation:

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