Question

13. The second angle of a triangle is 15° less than twice the first angle. The third angle is 20° more than
the second angle. Find the three angles​

Answer 1

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

Given:

• ∠A = ∠A
• ∠B = 2A - 15°
• ∠C = B + 20°

To Find:

Measurements of ∠A, ∠B, ∠C

Method:

It's given that: ∠C = B + 20°

Substituting for B;

∠C = (2A - 15) + 20°

⇒ ∠C = 2A + 5 ................ (Equation 1)

By Angle Sum Property;

∠A + ∠B + ∠C = 180°

Substituting for ∠A, ∠B, ∠C in the above Equation;

A + (2A - 15) + (2A + 5) = 180°

⇒ A + 2A - 15 + 2A + 5 = 180°

⇒ 5A - 10° = 180°

⇒ 5A = 180° + 10° = 190°

⇒ A = 190 / 5 = 38°

⇒ ∠A = 38°

Substituting ∠A in B & C;

B = 2A - 15

⇒ B = 2 × 38 - 15

⇒ ∠B = 61°

C = 2A + 5 ........... (From Equ 1)

⇒ C = 2 × 38 + 5

⇒∠C = 81°

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