83.0k views
4 votes
Hello help me with this question thanks in advance​

Hello help me with this question thanks in advance​-example-1
User Juster
by
7.9k points

2 Answers

12 votes

Answer:

1:c

2:a

3:d

4:b

5:d

Explanation:

In rhombus STAR


1.SAL\ \ TR
\left\{Characteristic\ of\ rhombus\right\}

SO < SKR=90°


2. < RAK=(1)/(2) < RAT=32°


3. < ARS+ < RAT=180°

< ARS=180°
- < RAT

=116°


4.\ < KRS=(1)/(2) < ARS

=58°


5.\ < SKR= < AKR= < SKT

= < AKT=90°

I hope this helps you

:)

User Pakorn
by
8.6k points
6 votes


\bold{\huge{\pink{\underline{ Solution }}}}

Solution 1 :-

The measure of Angle SKR is 90°

  • In Rhombus, The diagonals bisect each other at 90° it means diagonals are perpendicular to each other.

Hence, Option C is correct

Solution 2 :-

The measure of Angle RAK is 32°

  • We have given that angle RAT is 64° but here AK is acting as a bisector of Angle RAT

Therefore,


\sf{\angle{RAT = 2 }} {\sf{\angle{RAK}}}


\sf{( 64)/(2)}{\sf{=}}{\sf{\angle{RAK}}}


\sf{\angle{ RAK = 32°}}

Hence, Option a is correct

Solution 3 :-

The measure of Angle ARS is 116°

  • Opposite angles of rhombus are equal


\sf{\angle{ARS = }}{\sf{\angle{ATS}}}

So,


\sf{\angle{RSK = }}{\sf{\angle{RAK}}}


\sf{\angle{ RSK = 32° }}

By using Angle sum property

AngleRSA + AngleSAR + AngleARS = 180°


\sf{ 32° + 32° + }{\sf{\angle ARS = 180° }}


\sf{\angle {ARS = 180° - 64° }}


\sf{\angle{ARS = 116° }}

Hence, Option d is correct

Solution 4 :-

The measure of angle KRS is 58°

  • We know that angle ARS is 116° but here RK is acting as a bisector of Angle ARS

Therefore ,


\sf{\angle{ARS}}{\sf{ = 2}}{\sf{\angle KRS}}


\sf{( 116)/(2)}{\sf{=}}{\sf{\angle{KRS}}}


\sf{\angle{ KRS = 58°}}

Hence, Option b is correct

Solution 5 :-

mAngleSKR = All of the above

  • In rhombus, the diagonals bisect each other at 90°

From Above, we can say that,

mAngleSKR + mAngleAKR + mAngleAKT + mAngleSKT = 90°

Hence, Option D is correct.

User Guanlun
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories