Angle ABD and angle DBC are linear pairs, and angle ABD and angle EDC are vertical angles. If the measure of angle ABD=5(2x+1),

Question

3 months ago

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Angle ABD and angle DBC are linear pairs, and angle ABD and angle EDC are vertical angles. If the measure of angle ABD=5(2x+1),

the measure of angle DBC=3x+6, and the measure of angle EBC=y+135\2, select all the statements that are true A) measure of angle ABD=45 B.) measure of angle DBC=135 C.) x=13 D.)y=135 E.)measure of angle EDC =135 E.) measure of angle ABC + the measure of angle ABE=270 F.) angle DBC and angle EBC are linear pairs

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-02-25T01:41:43+03:00

∠ ABD = 5(2X+1)
∠ DBC = 3X+6
∠ EBC = Y +135/2

Angles ∠ ABD and ∠ DBC are considered linear pairs.
Thus, ∠ ABD +∠ DBC = 180,
leading to the equation 5(2X+1) + 3X+6 = 180, which we solve for x.
This gives x = 13. Consequently, ∠ ABD = 5(2X+1) = 5(2*13+1) = 135.
Similarly, ∠ DBC = 3x+6 = 3*13+6 = 45.

Angles ∠ ABD and ∠ EBC are vertical angles, so ∠ ABD = ∠ EBC = 135.
Therefore, y +135/2 = 135,
which means y = 135/2.

<span>The verified true statements are:
--------------------------------------</span><span>
C.) x=13
E.) Measure of angle EBC = 135
F.) Angle DBC and angle EBC are linear pairs.</span>

tester [12.3K] · Answer 2 · 2026-02-25T01:38:46+03:00

tester [12.3K]3 months ago

3 0

Answer:

What the responder stated is accurate, but y also equals 135.

Detailed explanation: