Mathematics

# In the adjoining Figure, $\overline{XY}\parallel \overline {BC}$. Find the values of $x, y, z$.

##### SOLUTION
Given that XY$||$BC
then,
In $\Delta ABC$
$\angle A+\angle B+\angle C=180^o$(property of triangle)
$40^o+30^o+\angle C=180^o$
$70^o+z=180^o$
$z=180^o-70^o$
$z=110^o$
$XY||BC$
then
$\angle x^o=\angle B$
$\angle x^o=30^o$.
Now, In $\Delta AXY$
$\angle x^o+\angle y^o+\angle A=180^o$(property of triangle)
$30^o+\angle y^o=40^o=180^o$
$\angle y^o=180^o-70^o$
$\angle y^o=110^o$

You're just one step away

Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
Find the complement of each of the following angles $24^{\circ}$
• A. $156^{\circ}$
• B. $36^{\circ}$
• C. None of these
• D. $66^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 23rd 09, 2020

Q2 Single Correct Medium
In the triangle ABC, the bisectors of exterior angles B and C meet at O. Given that $\angle BAC = 70^{\circ}$ and $\angle ACB C = 50^{\circ}$, find $\angle BOC$
• A. $46^o$
• B. $36^o$
• C. none of the above
• D. $55^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
Complement angle of
• A. $77.4^{\circ}$
• B. $67.3^{\circ}$
• C. $76.3^{\circ}$
• D. $77.3^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Single Correct Medium
If figure, $AB\parallel CD$. Determine $\angle a$
• A. $53^o$
• B. $73^o$
• C. $83^o$
• D. $93^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 23rd 09, 2020

Q5 Subjective Medium
Read the following two statements which are taken as axioms:
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $180^0$.