Lesson Worksheet: Angle Sum of a Triangle Mathematics • 8th Grade

In this worksheet, we will practice finding a missing angle in a triangle given the two other angles.

Q1:

The measures of the base angles of an isosceles triangle are (9π‘šβˆ’2𝑛)∘ and (5π‘š+2𝑛)∘, and the measure of the vertex angle is (4π‘š)∘. Find the values of π‘š and 𝑛.

  • Aπ‘š=10, 𝑛=10
  • Bπ‘š=13, 𝑛=13
  • Cπ‘š=10, 𝑛=20
  • Dπ‘š=13, 𝑛=26

Q2:

Find the measure of π‘₯.

Q3:

Complete the sentence: The measure of a straight angle is the sum of the measures of the interior angles of a triangle.

  • Agreater than
  • Bless than
  • Cequal to

Q4:

What is the sum of the measures of the two acute angles in a right-angled triangle?

Q5:

Calculate the value of π‘₯.

Q6:

In triangle 𝐴𝐡𝐢, π‘šβˆ π΄=78∘ and π‘šβˆ π΅=2π‘šβˆ πΆ. What is π‘šβˆ πΆ?

Q7:

Find π‘šβˆ π΄π΅πΆ.

Q8:

The given design is carved on a wooden board. If ∠𝐢 is a right angle, determine the values of π‘₯, 𝑦, and 𝑧.

  • Aπ‘₯=53, 𝑦=82, 𝑧=94
  • Bπ‘₯=36, 𝑦=82, 𝑧=53
  • Cπ‘₯=36, 𝑦=41, 𝑧=94
  • Dπ‘₯=53, 𝑦=41, 𝑧=53

Q9:

Determine the values of π‘₯ and 𝑦.

  • Aπ‘₯=90, 𝑦=90
  • Bπ‘₯=47, 𝑦=43
  • Cπ‘₯=43, 𝑦=47
  • Dπ‘₯=137, 𝑦=133

Q10:

In triangle 𝐴𝐡𝐢, π‘šβˆ π΄=54∘ and π‘šβˆ π΅=71∘. Find π‘šβˆ πΆ.

Q11:

In △𝐴𝐡𝐢, π‘šβˆ π΅=2π‘šβˆ π΄=40∘. Determine π‘šβˆ πΆ.

Q12:

In the figure below, given that 𝐴𝐡𝐢𝐷 is a rectangle, determine π‘šβˆ πΆπ·πΈ.

Q13:

If 𝐴𝐡𝐢 is a triangle in which π‘šβˆ π΄=79π‘šβˆ π΅ and π‘šβˆ πΆ=2π‘šβˆ π΄. Calculate the measures of angles 𝐴, 𝐡, and 𝐢.

  • Aπ‘šβˆ π΄=37∘, π‘šβˆ π΅=48∘, π‘šβˆ πΆ=95∘
  • Bπ‘šβˆ π΄=70∘, π‘šβˆ π΅=90∘, π‘šβˆ πΆ=20∘
  • Cπ‘šβˆ π΄=42∘, π‘šβˆ π΅=54∘, π‘šβˆ πΆ=84∘
  • Dπ‘šβˆ π΄=76∘, π‘šβˆ π΅=85∘, π‘šβˆ πΆ=19∘

Q14:

In the triangle 𝐴𝐡𝐢, π‘šβˆ π΄=ο€Ήπ‘₯+97ο…οŠ¨βˆ˜, π‘šβˆ π΅=(60βˆ’5π‘₯)∘, and π‘šβˆ πΆ=(59βˆ’7π‘₯)∘. Find the measure of each angle.

  • Aπ‘šβˆ π΄=133∘, π‘šβˆ π΅=30∘, π‘šβˆ πΆ=20∘
  • Bπ‘šβˆ π΄=133∘, π‘šβˆ π΅=30∘, π‘šβˆ πΆ=17∘
  • Cπ‘šβˆ π΄=133∘, π‘šβˆ π΅=25∘, π‘šβˆ πΆ=22∘
  • Dπ‘šβˆ π΄=157∘, π‘šβˆ π΅=20∘, π‘šβˆ πΆ=3∘
  • Eπ‘šβˆ π΄=122∘, π‘šβˆ π΅=35∘, π‘šβˆ πΆ=24∘

Q15:

Given that 𝐴𝐡𝐢 is a triangle in which π‘šβˆ π΄=(2π‘₯+6)∘, π‘šβˆ π΅=(3π‘₯+3)∘, and π‘šβˆ πΆ=(5π‘₯+6)∘, determine π‘šβˆ π΄.

Q16:

Find the measure of each angle in the triangle below.

  • A90∘, 47∘, 43∘
  • B90∘, 42∘, 48∘
  • C90∘, 45∘, 45∘
  • D90∘, 52∘, 38∘

Q17:

The figure shows a rectangle 𝐴𝐡𝐢𝐷 and a square π΄π΅π‘Œπ‘‹. What is π‘šβˆ π΄π‘Œπ·?

Q18:

The sum of the measures of the angles of a triangle is 180∘. In a right triangle, what is the sum of the measures of the two acute angles?

Q19:

In △𝐽𝐿𝑃, π‘šβˆ π½π‘€π‘ƒ=(5π‘₯βˆ’9)∘. If 𝐽𝑀 is an altitude of △𝐽𝐿𝑃, find π‘₯.

Q20:

If the ratio between the measures of the angles of a triangle is 11∢18∢7, determine the measures of the angles.

  • A55∘, 73∘, 62∘
  • B55∘, 90∘, 35∘
  • C16∘, 23∘, 12∘
  • D55∘, 60∘, 65∘
  • E35∘, 70∘, 105∘

Q21:

Suppose that in the figure, π‘šβˆ πΏ=2π‘₯∘ and π‘šβˆ πΎ=4π‘₯∘. Determine these two angles.

  • Aπ‘šβˆ πΏ=30∘, π‘šβˆ πΎ=120∘
  • Bπ‘šβˆ πΏ=30∘, π‘šβˆ πΎ=60∘
  • Cπ‘šβˆ πΏ=60∘, π‘šβˆ πΎ=120∘
  • Dπ‘šβˆ πΏ=60∘, π‘šβˆ πΎ=30∘
  • Eπ‘šβˆ πΏ=120∘, π‘šβˆ πΎ=60∘

Q22:

The measures of the angles in a triangle are in a ratio of 3∢2∢5. Work out the measures of these angles.

  • A54∘, 36∘, 90∘
  • B30∘, 50∘, 100∘
  • C50∘, 78∘, 52∘
  • D54∘, 30∘, 96∘
  • E30∘, 20∘, 50∘

Q23:

Is the measure of a straight angle equal to the sum of the measures of the angles of a triangle?

  • ANo
  • BYes

Q24:

𝐴𝐡𝐢 is a triangle in which 𝐢𝐷 bisects ∠𝐡𝐢𝐴. If π‘šβˆ π΄=62∘ and π‘šβˆ π΄π·πΆ=81∘, find π‘šβˆ π΅.

Q25:

What is π‘₯?

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