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Chapter 2: Q. 200 (page 144)

The measure of the smallest

angle of a right triangle is 20掳

less than the measure of the next

larger angle. Find the measures of

all three angles.

Short Answer

Expert verified

The three angles measures35掳,55掳and90掳.

Step by step solution

01

Given information:

Let the larger angle 鈭�Abe a掳,

then the smallest angle 鈭�Bwill be a掳-20掳.

Also, third angle鈭�Cis90掳(Right triangle)

02

Step 2:

Formula:鈭�A+鈭�B+鈭�C=180掳

03

Step 3:

Substitute:a掳+(a掳-20掳)+90掳=180掳

04

Step 4:

On solving:

2a掳+70掳=180掳2a掳=180掳-70掳2a掳=110掳a掳=110掳2=55掳

05

Step 5:

From Step 1, Given 鈭�A=a掳=55掳

鈭�B=a掳-20掳=55掳-20掳=35掳.

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