Name: Angle Sum Property of a Quadrilateral
Uploaded: 2019-07-19
Duration: 7 min 55 s
Description: We know that quadrilaterals have four sides and four angles. To know more about what makes the angles of a quadrilateral special, involve yourself with this...

Question

Here are three angles. Two of the angles are equal. The diagram shows one angle of $100 °$ . Calculate the other two angles. There are two possible answers.

Accepted Answer

We have given three angles in which two angles are equal and one angle is $100 °$ .

Let the other two unknown angles be $x °$ and $y °$ .

We can see that all the given three angles form a complete angle, and we know that a complete angle is equal to $360 °$ . i.e.

$100 ° + x ° + y ° = 360 °$

We have given two angles are equal, so if the angles $x °$ and $y °$ are equal, then-

$\Rightarrow 100 ° + x ° + x ° = 360 ° \Rightarrow 2 x ° = 360 ° - 100 ° = 260 ° \Rightarrow x ° = \frac{260 °}{2} = 130 °$

It means if the unknown angles are equal. then the measure of both of them is $130 °$ .

Now, if $x °$ or $y °$ is equal to $100 °$ , then-

$\Rightarrow 100 ° + 100 ° + x ° or y ° = 360 ° \Rightarrow x ° or y ° = 360 ° - 200 ° = 160 °$

Hence, the two angles can be of $130 °$ or $100 °$ and $160 °$ .

Lynn Byrd, Greg Byrd and, Chris Pearce Solutions for Chapter: Angles and Constructions, Exercise 5: Check your progress

Lynn Byrd Mathematics Solutions for Exercise - Lynn Byrd, Greg Byrd and, Chris Pearce Solutions for Chapter: Angles and Constructions, Exercise 5: Check your progress

Questions from Lynn Byrd, Greg Byrd and, Chris Pearce Solutions for Chapter: Angles and Constructions, Exercise 5: Check your progress with Hints & Solutions

Learn and Prepare for any exam you want !