50035

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

585

Question

Triangle ABCABC is an isosceles triangle.



What is the size of the angle ∠\angleABCABC ?

Worked Solution

Let  x\large x = ∠\angleABCABC = ∠\angleBCABCA (isosceles)
x\large x + x\large x + 65 = 180
2x\large x = 115
∴x\therefore \large x = 57.5°

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Triangle $ABC$ is an isosceles triangle.
sm_img //teacher.smartermaths.com.au/wp-content/uploads/2016/12/naplan-2015-12mc.png 220 indent3 vpad
What is the size of the angle $\angle$$ABC$ ?
workedSolution
sm_nogap Let  $\large x$ = $\angle$$ABC$ = $\angle$$BCA$ ` ` (isosceles)
| | | | -----------------------: | -------------------------------------------- | | $\large x$ + $\large x$ + 65 | = 180 | | 2$\large x$ | = 115 | | $\therefore \large x$ | = {{{correctAnswer}}} |
correctAnswer
57.5°

Answers

Is Correct?Answer
x

32.5°

x

45°

✓

57.5°

x

60°

Variant 1

DifficultyLevel

584

Question

Triangle ABCABC is an isosceles triangle.



What is the size of the angle ∠\angleABCABC ?

Worked Solution

Let  x\large x = ∠\angleABCABC = ∠\angleBACBAC (Base angles of an isosceles Δ\Delta equal)
2x\large x + 40 = 180
2x\large x = 140
∴x\therefore \large x = 70°

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Triangle $ABC$ is an isosceles triangle.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2023/01/Geom_50035_v1.svg 200 indent3 vpad
What is the size of the angle $\angle$$ABC$ ?
workedSolution
sm_nogap Let  $\large x$ = $\angle$$ABC$ = $\angle$$BAC$ ` ` (Base angles of an isosceles $\Delta$ equal)
| | | | -----------------------: | -------------------------------------------- | | 2$\large x$ + 40 | = 180 | | 2$\large x$ | = 140 | | $\therefore \large x$ | = {{{correctAnswer}}} |
correctAnswer
70°

Answers

Is Correct?Answer
x

50°

✓

70°

x

110°

x

140°

Variant 2

DifficultyLevel

583

Question

Triangle ABCABC is an isosceles triangle.



What is the size of the angle ∠\angleABCABC ?

Worked Solution

Let  x\large x = ∠\angleABCABC = ∠\angleBCABCA (Base angles of an isosceles Δ\Delta equal)
2x\large x + 64 = 180
2x\large x = 116
∴x\therefore \large x = 58°

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Triangle $ABC$ is an isosceles triangle.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2023/01/Geom_50035_v2.svg 220 indent3 vpad
What is the size of the angle $\angle$$ABC$ ?
workedSolution
sm_nogap Let  $\large x$ = $\angle$$ABC$ = $\angle$$BCA$ ` ` (Base angles of an isosceles $\Delta$ equal)
| | | | -----------------------: | -------------------------------------------- | | 2$\large x$ + 64 | = 180 | | 2$\large x$ | = 116 | | $\therefore \large x$ | = {{{correctAnswer}}} |
correctAnswer
58°

Answers

Is Correct?Answer
✓

58°

x

64°

x

116°

x

122°

Variant 3

DifficultyLevel

582

Question

Triangle ABCABC is an isosceles triangle.



What is the size of the angle ∠\angleABCABC ?

Worked Solution

Let  x\large x = ∠\angleABCABC = ∠\angleBACBAC (Base angles of an isosceles Δ\Delta equal)
2x\large x + 44 = 180
2x\large x = 136
∴x\therefore \large x = 68°

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Triangle $ABC$ is an isosceles triangle.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2023/01/Geom_50035_v3.svg 200 indent3 vpad
What is the size of the angle $\angle$$ABC$ ?
workedSolution
sm_nogap Let  $\large x$ = $\angle$$ABC$ = $\angle$$BAC$ ` ` (Base angles of an isosceles $\Delta$ equal)
| | | | -----------------------: | -------------------------------------------- | | 2$\large x$ + 44 | = 180 | | 2$\large x$ | = 136 | | $\therefore \large x$ | = {{{correctAnswer}}} |
correctAnswer
68°

Answers

Is Correct?Answer
x

136°

x

112°

✓

68°

x

44°

Variant 4

DifficultyLevel

581

Question

Triangle ABCABC is an isosceles triangle.



What is the size of the angle ∠\angleABCABC ?

Worked Solution

Let  x\large x = ∠\angleABCABC = ∠\angleBCABCA (Base angles of an isosceles Δ\Delta equal)
2x\large x + 152 = 180
2x\large x = 28
∴x\therefore \large x = 14°

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Triangle $ABC$ is an isosceles triangle.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2023/01/Geom_50035_v4.svg 280 indent3 vpad
What is the size of the angle $\angle$$ABC$ ?
workedSolution
sm_nogap Let  $\large x$ = $\angle$$ABC$ = $\angle$$BCA$ ` ` (Base angles of an isosceles $\Delta$ equal)
| | | | -----------------------: | -------------------------------------------- | | 2$\large x$ + 152 | = 180 | | 2$\large x$ | = 28 | | $\therefore \large x$ | = {{{correctAnswer}}} |
correctAnswer
14°

Answers

Is Correct?Answer
x

152°

x

76°

x

28°

✓

14°

Variant 5

DifficultyLevel

580

Question

Triangle ABCABC is an isosceles triangle.



What is the size of the angle ∠\angleABCABC ?

Worked Solution

Let  x\large x = ∠\angleABCABC = ∠\angleBACBAC (Base angles of an isosceles Δ\Delta equal)
2x\large x + 106 = 180
2x\large x = 74
∴x\therefore \large x = 37°

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Triangle $ABC$ is an isosceles triangle.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2023/01/Geom_50035_v5.svg 200 indent3 vpad
What is the size of the angle $\angle$$ABC$ ?
workedSolution
sm_nogap Let  $\large x$ = $\angle$$ABC$ = $\angle$$BAC$ ` ` (Base angles of an isosceles $\Delta$ equal)
| | | | -----------------------: | -------------------------------------------- | | 2$\large x$ + 106 | = 180 | | 2$\large x$ | = 74 | | $\therefore \large x$ | = {{{correctAnswer}}} |
correctAnswer
37°

Answers

Is Correct?Answer
✓

37°

x

74°

x

106°

x

143°

Tags